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2004•Proceedings of the American Mathematical SocietyOpen access

Enlarging totally geodesic submanifolds of symmetric spaces to minimal submanifolds of one dimension higher

Cláudio Gorodski

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Abstract

We show that a totally geodesic submanifold of a symmetric space satisfying certain conditions admits an extension to a minimal submanifold of dimension one higher, and we apply this result to construct new examples of complete embedded minimal submanifolds in simply connected noncompact globally symmetric spaces.

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What this paper is about

We show that a totally geodesic submanifold of a symmetric space satisfying certain conditions admits an extension to a minimal submanifold of dimension one higher, and we apply this result to construct new examples of complete embedded minimal submanifolds in simply connected noncompact globally symmetric spaces.

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Available abstract

We show that a totally geodesic submanifold of a symmetric space satisfying certain conditions admits an extension to a minimal submanifold of dimension one higher, and we apply this result to construct new examples of complete embedded minimal submanifolds in simply connected noncompact globally symmetric spaces.

Key concepts: Submanifold, Totally geodesic, Mathematics, Dimension (graph theory), Pure mathematics, Geodesic, Symmetric space, Extension (predicate logic)

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