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Stable Submanifolds in the Product of Projective Spaces

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Abstract

We provide a classification theorem for compact stable minimal immersions (CSMI) of codimension 1 or dimension 1 (codimension 1 and 2 or dimension 1 and 2) in the product of a complex (quaternionic) projective space with any other Riemannian manifold. We characterize the complex minimal immersions of codimension 2 or dimension 2 as the only CSMI in the product of two complex projective spaces. As an application, we characterize the CSMI of codimension 1 or dimension 1 (codimension 1 and 2 or dimension 1 and 2) in the product of a complex (quaternionic) projective space with any compact rank one symmetric space.

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  1. Department of Mathematics, Universidad del Valle, Calle 13 100-00, Cali, 760032, Colombia

    Alejandra Ramirez-Luna

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  1. Alejandra Ramirez-Luna
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Correspondence to Alejandra Ramirez-Luna.

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The author was sponsored by the International Mathematical Union and the World Academy of Sciences under the PhD scholarship IMU Breakout Graduate Fellowship 2016. I am very grateful for the patience and guidance of Professors Gonzalo García, Fernando Marques, and Heber Mesa. Part of this work was done while the author was visiting Princeton University as a VSRC. I am grateful to Princeton University for the hospitality. I am also thankful to the Department of Mathematics at Universidad del Valle for partial support my visit to Princeton. Finally, I thank Shuli Chen for comments on this work.

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Ramirez-Luna, A. Stable Submanifolds in the Product of Projective Spaces. J Geom Anal 32, 227 (2022). https://doi.org/10.1007/s12220-022-00965-5

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  • DOI: https://doi.org/10.1007/s12220-022-00965-5

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