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Complete area minimizing minimal surfaces which are not totally geodesic. (English) Zbl 0534.53004

Pac. J. Math. 111, 35-38 (1984).

Author’s introduction: ”If a 3-manifold has non-negative Ricci curvature, then a complete area minimizing minimal surface in the 3-manifold is totally geodesic. The main theorem gives a method of constructing non- totally geodesic examples of such surfaces in certain manifolds which do not satisfy the Ricci curvature conditions. In particular, examples are described for hyperbolic space.”

Reviewer: D.Ferus

Cited in 1 Document

MSC:

53A10	Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
53C42	Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)

Keywords:

incompressible surface; Ricci curvature; minimal surface; totally geodesic; non-totally geodesic examples

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