An isometrical CPn-theorem |
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Authors: | Xiaole SU Hongwei SUN Yusheng WANG |
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Institution: | 1. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems (Beijing Normal University), Ministry of Education, Beijing 100875, China2. School of Mathematical Sciences, Capital Normal University, Beijing 100037, China |
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Abstract: | Let be a complete Riemannian manifold with , and let be two complete totally geodesic submanifolds in M. We prove that if n1 + n2 = n − 2 and if the distance , then Mi is isometric to , or with the canonical metric when ni>0, and thus, M is isometric to , or except possibly when n = 3 and M1 (or M2) with or n = 4 and M1 (or M2) . |
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Keywords: | Rigidity positive sectional curvature totally geodesic submanifolds |
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