Rigidity results on totally real submanifolds in complex space forms

Dang Van Cuong; Nguyen Thac Dung; Nguyen Thi Kim Son

doi:10.1215/21562261-2023-0006

May 2024 Rigidity results on totally real submanifolds in complex space forms

Dang Van Cuong, Nguyen Thac Dung, Nguyen Thi Kim Son

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Abstract

We study n-dimensional totally real minimal submanifolds M immersed in complex space forms ${\tilde{M}}^{n} (c)$ for $c \leq 0$ . We prove that M is totally geodesic if the $L^{2 p}$ -norm of the second fundamental form is finite for some $p \in R$ . We also derive vanishing results for the space of harmonic forms on such submanifolds.

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Dang Van Cuong, Nguyen Thac Dung, and Nguyen Thi Kim Son "Rigidity results on totally real submanifolds in complex space forms," Kyoto Journal of Mathematics 64(2), 261-276, (May 2024). https://doi.org/10.1215/21562261-2023-0006

Received: 19 March 2021; Accepted: 20 January 2022; Published: May 2024

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