On complete maximal submanifolds in pseudo-hyperbolic space

Andrea Seppi; Graham Smith; J\'er\'emy Toulisse

On complete maximal submanifolds in pseudo-hyperbolic space

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arxiv 2305.15103 v1 pith:S6QEG2SN submitted 2023-05-24 math.DG math.GT

Andrea Seppi , Graham Smith , Jérémy Toulisse This is my paper · ORCID

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keywords completemaximalpseudo-hyperbolicspacesubmanifoldstheoryanosovapplications

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abstract

We provide a full classification of complete maximal $p$-dimensional spacelike submanifolds in the pseudo-hyperbolic space $\mathbf{H}^{p,q}$, and we study its applications to Teichm\"uller theory and to the theory of Anosov representations of hyperbolic groups in $\mathsf{PO}(p,q+1)$.

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Equiaffine immersions and pseudo-Riemannian space forms
math.DG 2025-12 conditional novelty 7.0 of 10

A new explicit correspondence shows that maximal spacelike submanifolds in pseudo-hyperbolic space are equivalent to proper affine spheres, yielding new boundary constructions and a generalized harmonic Blaschke lift.

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