{"id":41047,"date":"2024-09-25T23:19:58","date_gmt":"2024-09-25T23:19:58","guid":{"rendered":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%ae%d8%a7%d9%86%d9%88%d8%a7%d8%af%d9%87-%d8%a7%db%8c-%d8%a7%d8%b2-kahler-flying-wing-ricci-solitons\/"},"modified":"2024-09-26T06:23:15","modified_gmt":"2024-09-26T06:23:15","slug":"%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%ae%d8%a7%d9%86%d9%88%d8%a7%d8%af%d9%87-%d8%a7%db%8c-%d8%a7%d8%b2-kahler-flying-wing-ricci-solitons","status":"publish","type":"product","link":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%ae%d8%a7%d9%86%d9%88%d8%a7%d8%af%d9%87-%d8%a7%db%8c-%d8%a7%d8%b2-kahler-flying-wing-ricci-solitons\/","title":{"rendered":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u062e\u0627\u0646\u0648\u0627\u062f\u0647 \u0627\u06cc \u0627\u0632 K\u00e4hler Flying Wing Ricci Solitons"},"content":{"rendered":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nA family of K\u00e4hler flying wing steady Ricci solitons<\/td>\n<\/tr>\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u062e\u0627\u0646\u0648\u0627\u062f\u0647 \u0627\u06cc \u0627\u0632 K\u00e4hler Flying Wing Ricci Solitons<\/td>\n<\/tr>\n
\u0646\u0648\u06cc\u0633\u0646\u062f\u06af\u0627\u0646 <\/td>\nPak-Yeung Chan, Ronan J. Conlon, Yi Lai<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nPDF<\/td>\n<\/tr>\n
\u0632\u0628\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u062a\u062d\u0648\u06cc\u0644\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u062a\u0631\u062c\u0645\u0647 \u0634\u062f\u0647 <\/td>\n\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\n<\/tr>\n
\u0646\u062d\u0648\u0647 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 <\/td>\n\u062f\u0648 \u062a\u0627 \u0633\u0647 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634 (\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u062f\u0627\u0646\u0644\u0648\u062f\u06cc)<\/td>\n<\/tr>\n
\u062a\u0639\u062f\u0627\u062f \u0635\u0641\u062d\u0627\u062a<\/td>\n48<\/td>\n<\/tr>\n
\u0644\u06cc\u0646\u06a9 \u062f\u0627\u0646\u0644\u0648\u062f \u0631\u0627\u06cc\u06af\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc<\/td>\n\u062f\u0627\u0646\u0644\u0648\u062f \u0645\u0642\u0627\u0644\u0647<\/a><\/td>\n<\/tr>\n
\u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u0645\u0648\u0636\u0648\u0639\u0627\u062a <\/td>\nDifferential Geometry,\u0647\u0646\u062f\u0633\u0647 \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 ,<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a <\/td>\nSubmitted 6 March, 2024; originally announced March 2024. , MSC Class: 53E20; 53E30<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u0627\u0631\u0633\u0627\u0644 6 \u0645\u0627\u0631\u0633 2024 \u061b\u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u0645\u0627\u0631\u0633 2024 \u0627\u0639\u0644\u0627\u0645 \u0634\u062f \u060c \u06a9\u0644\u0627\u0633 MSC: 53E20 \u061b53e30<\/td>\n<\/tr>\n
\u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u062f\u0631 \u067e\u0627\u06cc\u06af\u0627\u0647 \u0647\u0627\u06cc \u0639\u0644\u0645\u06cc <\/td>\n\n INSPIRE HEP<\/a>
\n
\n NASA ADS<\/a>
\n
\n Google Scholar<\/a>
\n
\n Semantic Scholar<\/a>
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\n arXiv<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n

\u0686\u06a9\u06cc\u062f\u0647<\/h2>\n

In $1996$, H.-D. Cao constructed a $U(n)$-invariant steady gradient K\u00e4hler-Ricci soliton on $\\mathbb{C}^{n}$ and asked whether every steady gradient K\u00e4hler-Ricci soliton of positive curvature on $\\mathbb{C}^{n}$ is necessarily $U(n)$-invariant (and hence unique up to scaling). Recently, Apostolov-Cifarelli answered this question in the negative for $n=2$. Here, we construct a family of $U(1)\\times U(n-1)$-invariant, but not $U(n)$-invariant, complete steady gradient K\u00e4hler-Ricci solitons with strictly positive curvature operator on real $(1,\\,1)$-forms (in particular, with strictly positive sectional curvature) on $\\mathbb{C}^{n}$ for $n\\geq3$, thereby answering Cao’s question in the negative for $n\\geq3$. This family of steady Ricci solitons interpolates between Cao’s $U(n)$-invariant steady K\u00e4hler-Ricci soliton and the product of the cigar soliton and Cao’s $U(n-1)$-invariant steady K\u00e4hler-Ricci soliton. This provides the K\u00e4hler analog of the Riemannian flying wings construction of Lai. In the process of the proof, we also demonstrate that the almost diameter rigidity of $\\mathbb{P}^{n}$ endowed with the Fubini-Study metric does not hold even if the curvature operator is bounded below by $2$ on real $(1,\\,1)$-forms.<\/p>\n

\u0686\u06a9\u06cc\u062f\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc (\u062a\u0631\u062c\u0645\u0647 \u0645\u0627\u0634\u06cc\u0646\u06cc)<\/h2>\n

\u062f\u0631 $ 1996 $ \u060c H.-D.CAO \u06cc\u06a9 $ u (n) $-\u062b\u0627\u0628\u062a \u06af\u0631\u0627\u062f\u06cc\u0627\u0646 \u062b\u0627\u0628\u062a k\u00e4hler-ricci soliton \u062f\u0631 $ \\ mathbb {c}^{n} $ \u0633\u0627\u062e\u062a \u0648 \u067e\u0631\u0633\u06cc\u062f \u06a9\u0647 \u0622\u06cc\u0627 \u0647\u0631 \u0634\u06cc\u0628 \u067e\u0627\u06cc\u062f\u0627\u0631 k\u00e4hler-ricci soliton \u0627\u0632 $ \\ mathbb {c}^^{n} $ \u0644\u0632\u0648\u0645\u0627 $ u (n) $-\u062b\u0627\u0628\u062a (\u0648 \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648 \u0645\u0646\u062d\u0635\u0631 \u0628\u0647 \u0641\u0631\u062f \u062a\u0627 \u0645\u0642\u06cc\u0627\u0633 \u0628\u0646\u062f\u06cc) \u0627\u0633\u062a.\u0628\u0647 \u062a\u0627\u0632\u06af\u06cc \u060c Apostolov-Cifarelli \u0628\u0647 \u0627\u06cc\u0646 \u0633\u0624\u0627\u0644 \u062f\u0631 \u0645\u0646\u0641\u06cc \u0628\u0631\u0627\u06cc $ n = 2 $ \u067e\u0627\u0633\u062e \u062f\u0627\u062f.\u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u060c \u0645\u0627 \u06cc\u06a9 \u062e\u0627\u0646\u0648\u0627\u062f\u0647 $ u (1) \\ \\ u (n-1) $-\u062b\u0627\u0628\u062a \u060c \u0627\u0645\u0627 $ u (n) $-\u062b\u0627\u0628\u062a \u060c \u0634\u06cc\u0628 \u06a9\u0627\u0645\u0644 \u0648 \u0634\u06cc\u0628 \u06a9\u0627\u0645\u0644 K\u00e4hler-ricci \u0628\u0627 \u0627\u067e\u0631\u0627\u062a\u0648\u0631 \u0627\u0646\u062d\u0646\u0627\u06cc \u06a9\u0627\u0645\u0644\u0627\u064b \u0645\u062b\u0628\u062a \u0628\u0631 \u0631\u0648\u06cc $ $ \u0645\u06cc \u0633\u0627\u0632\u06cc\u0645.(1 \u060c \\ \u060c 1) $-\u0641\u0631\u0645 \u0647\u0627 (\u0628\u0647 \u0648\u06cc\u0698\u0647 \u060c \u0628\u0627 \u0627\u0646\u062d\u0646\u0627\u06cc \u0645\u0642\u0637\u0639\u06cc \u06a9\u0627\u0645\u0644\u0627\u064b \u0645\u062b\u0628\u062a) \u062f\u0631 $ \\ mathbb {c}^{n} $ \u0628\u0631\u0627\u06cc $ n \\ geq3 $ \u060c \u062f\u0631 \u0646\u062a\u06cc\u062c\u0647 \u0628\u0647 \u0633\u0624\u0627\u0644 CAO \u062f\u0631 \u0645\u0646\u0641\u06cc \u0628\u0631\u0627\u06cc $ n \\ \u067e\u0627\u0633\u062e \u0645\u06cc \u062f\u0647\u062fGEQ3 $.\u0627\u06cc\u0646 \u062e\u0627\u0646\u0648\u0627\u062f\u0647 \u0627\u0632 \u0633\u0648\u0644\u06cc\u062a\u0648\u0646 \u0647\u0627\u06cc Ricci \u067e\u0627\u06cc\u062f\u0627\u0631 \u0628\u06cc\u0646 $ u (n) $ cao-\u062b\u0627\u0628\u062a k\u00e4hler-ricci soliton \u0648 \u0645\u062d\u0635\u0648\u0644 \u0633\u06cc\u06af\u0627\u0631 \u062d\u0644\u06cc\u062a\u0648\u0646 \u0648 $ $ u (n-1) $-\u062b\u0627\u0628\u062a $-\u062b\u0627\u0628\u062a K\u00e4hler-Irricci Soliton \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f.\u0627\u06cc\u0646 \u0622\u0646\u0627\u0644\u0648\u06af K\u00e4hler \u0627\u0632 \u0633\u0627\u062e\u062a \u0628\u0627\u0644 \u0647\u0627\u06cc \u067e\u0631\u0648\u0627\u0632 \u0631\u06cc\u0645\u0627\u0646\u06cc\u0627\u0646 LAI \u0631\u0627 \u0641\u0631\u0627\u0647\u0645 \u0645\u06cc \u06a9\u0646\u062f.\u062f\u0631 \u0641\u0631\u0622\u06cc\u0646\u062f \u0627\u062b\u0628\u0627\u062a \u060c \u0645\u0627 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u06a9\u0647 \u0627\u0633\u062a\u062d\u06a9\u0627\u0645 \u062a\u0642\u0631\u06cc\u0628\u0627 \u0642\u0637\u0631 $ \\ Mathbb {p}^{n} $ \u0648\u0642\u0641 \u0628\u0627 \u0645\u062a\u0631\u06cc\u06a9 \u0641\u0648\u0628\u06cc\u0646\u06cc-\u0645\u0637\u0627\u0644\u0639\u0647 \u062d\u062a\u06cc \u0627\u06af\u0631 \u0627\u067e\u0631\u0627\u062a\u0648\u0631 \u0627\u0646\u062d\u0646\u0627\u06cc \u0632\u06cc\u0631 2 \u062f\u0644\u0627\u0631 \u062f\u0631 \u0648\u0627\u0642\u0639\u06cc \u0645\u062d\u062f\u0648\u062f \u0634\u0648\u062f$ (1 \u060c \\ \u060c 1) $-\u0641\u0631\u0645.<\/p>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n","protected":false},"excerpt":{"rendered":"

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