A convergence theorem for Riemannian submanifolds

Author:
Zhong Min Shen

Journal:
Trans. Amer. Math. Soc. **347** (1995), 1343-1350

MSC:
Primary 53C20; Secondary 53C15, 53C23, 53C30, 53C40

DOI:
https://doi.org/10.1090/S0002-9947-1995-1254853-0

MathSciNet review:
1254853

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we study the convergence of Riemannian submanifolds. In particular, we prove that any sequence of closed submanifolds with bounded normal curvature and volume in a closed Riemannian manifold subconverge to a closed submanifold in the topology. We also obtain some applications to irreducible homogeneous manifolds and pseudo-holomorphic curves in symplectic manifolds.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1995-1254853-0

Keywords:
Riemannian submanifold,
convergence in the topology,
normal curvature,
volume,
isoperimetric inequality,
injectivity radius,
pseudo-holomorphic curve,
homogeneous manifold

Article copyright:
© Copyright 1995
American Mathematical Society