A remark on positively curved manifolds of dimensions 7 and 13
I.A. Taimanov

TL;DR
This paper constructs infinitely many closed 7-manifolds as totally geodesic submanifolds within 13-dimensional positively curved closed Riemannian manifolds and discusses related geometric embedding problems.
Contribution
It introduces new constructions of totally geodesic embeddings of 7-manifolds into 13-dimensional positively curved manifolds and explores related geometric questions.
Findings
Existence of infinitely many such embeddings
Discussion on pinching constants
Analysis of other potential embeddings
Abstract
Totally geodesically embeddings of infinitely many closed 7-manifolds into 13-dimensional positively curved closed Riemannian manifolds are constructed. The problems of computing pinching constants and existence of other totally geodesical embeddings are discussed.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Morphological variations and asymmetry · Point processes and geometric inequalities
