A Pinching Theorem for Compact Minimal Submanifolds in Warped Products I × f S m ( c )

Xin Zhan and Zhonghua Hou
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Xin Zhan: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
Zhonghua Hou: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

Mathematics, 2020, vol. 8, issue 9, 1-16

Abstract: Let S m ( c ) be a Euclidean sphere of curvature c > 0 and R be a Euclidean line. We prove a pinching theorem for compact minimal submanifolds immersed in Riemannian warped products of the type I × f S m ( c ) , where f : I ? R + is a smooth positive function on an open interval I of R . This allows us to generalize Chen-Cui’s pinching theorem from Riemannian products S m ( c ) × R to Riemannian warped products I × f S m ( c ) .

Keywords: Riemannian warped product; DDVV Conjecture; pinching theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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