Betti and Tachibana numbers
S.E. Stepanov, J. Mike\v{s}
TL;DR
This paper introduces Tachibana numbers as an analog of Betti numbers on Riemannian manifolds, exploring their properties, classifications, and relationships with Betti numbers.
Contribution
It defines Tachibana numbers, analyzes their properties, and establishes connections with Betti numbers on Riemannian manifolds.
Findings
Tachibana numbers are characterized by specific conditions.
Connections between Betti and Tachibana numbers are established.
Properties of conformal Killing forms are analyzed.
Abstract
We present a rough classification of differential forms on a Riemannian manifold, we consider definitions and properties of conformal Killing forms on a compact Riemannian manifold and define Tachibana numbers as an analog of the well known Betti numbers. We state the conditions that characterize these numbers. In the last section we show connections between the Betti and Tachibana numbers.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Topological and Geometric Data Analysis · Geometry and complex manifolds