Real hypersurfaces in Kähler manifolds
Copyright policy )Real hypersurfaces in Kähler manifolds
This paper is concerned with the geometry of embedded real hypersurfaces in a Kähler manifold, where isomorphisms are both holomorphic and isometric in the underlying Riemannian structure. The author introduces their local invariants and compatibility relations, solves the local realization problem, and gives a characterization of the metric sphere in \(\mathbb C^n\) via a maximum principle for an adapted Laplace operator.
adapted frames, ambient manifold, Hermitian, Global differential geometry of Hermitian and Kählerian manifolds, Levi-Civita connection, local invariants, horizontal tangent bundle, embedding, holomorphic isometric isomorphisms, compatibility relations, embedded real hypersurfaces, compact strictly pseudoconvex hypersurface, CR manifolds, Gauss equations, Global submanifolds, Riemannian second fundamental form, Kähler metric, second covariant derivatives, Kähler manifold, adapted Laplace operator, doubly covariant tensor, horizontal mean curvature, Codazzi equations, Embeddings of CR manifolds, maximum principle, Real submanifolds in complex manifolds, commutator relations
adapted frames, ambient manifold, Hermitian, Global differential geometry of Hermitian and Kählerian manifolds, Levi-Civita connection, local invariants, horizontal tangent bundle, embedding, holomorphic isometric isomorphisms, compatibility relations, embedded real hypersurfaces, compact strictly pseudoconvex hypersurface, CR manifolds, Gauss equations, Global submanifolds, Riemannian second fundamental form, Kähler metric, second covariant derivatives, Kähler manifold, adapted Laplace operator, doubly covariant tensor, horizontal mean curvature, Codazzi equations, Embeddings of CR manifolds, maximum principle, Real submanifolds in complex manifolds, commutator relations
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