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This article shows that for generic choice of Riemannian metric on a compact oriented manifold M of dimension four, the tangent planes at any self-intersection $$p \in M$$ p ∈ M… Click to show full abstract
This article shows that for generic choice of Riemannian metric on a compact oriented manifold M of dimension four, the tangent planes at any self-intersection $$p \in M$$ p ∈ M of any prime closed parametrized minimal surface in M are not simultaneously complex for any orthogonal complex structure on M at p . This implies via geometric measure theory that $$H_2(M;{{\mathbb {Z}}})$$ H 2 ( M ; Z ) is generated by homology classes that are represented by oriented imbedded minimal surfaces.
Keywords:
self intersections;
minimal surfaces;
surfaces generic;
intersections closed;
closed parametrized;
parametrized minimal
Journal Title: Annals of Global Analysis and Geometry
Year Published: 2020
Link to full text (if available)
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Journal Title: Annals of Global Analysis and Geometry
Year Published: 2020
Link to full text (if available)
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recommendations!