Compact Minimal Submanifolds in a Large Class of Riemannian Manifolds

Through a new technique, we provide uniqueness, rigidity and non-existence results for compact minimal submanifolds of arbitrary dimension in a large class of Riemannian manifolds, which include between others, Riemannian double-twisted and warped products. Moreover, we show that our results can be...

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Bibliographic Details
Published in:Mediterranean journal of mathematics 2023-04, Vol.20 (2), Article 74
Main Authors: Herrera, J., Rubio, R. M., Salamanca, J. J.
Format: Article
Language:English
Subjects:
Manifolds (mathematics)
Mathematics
Mathematics and Statistics
Riemann manifold
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Summary:Through a new technique, we provide uniqueness, rigidity and non-existence results for compact minimal submanifolds of arbitrary dimension in a large class of Riemannian manifolds, which include between others, Riemannian double-twisted and warped products. Moreover, we show that our results can be applied in particular, to space forms and Cartan–Hadamard manifolds, re-obtaining several classic results in a different approach. Interesting applications to Geometric Analysis are also showed.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-023-02265-w