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Betti and Tachibana numbers of compact Riemannian manifolds. (English) Zbl 1279.53037

Summary: We present definitions and properties of conformal Killing forms on a Riemannian manifold and determine Tachibana numbers as analogs of the well-known Betti numbers of a compact Riemannian manifold. We show some sets of conditions which characterize these numbers. Finally, we prove some results which establish relationships between Betti and Tachibana numbers.

MSC:

53C20 Global Riemannian geometry, including pinching
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
53C24 Rigidity results
57R20 Characteristic classes and numbers in differential topology
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