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Betti and Tachibana numbers of compact Riemannian manifolds |
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| Authors: | Sergey E Stepanov Josef Mike? |
| Institution: | 1. Department of Mathematics, Finance University under the Government of Russian Federation, 125468 Moscow, Leningradsky Prospect, 49-55, Russian Federation;2. Department of Algebra and Geometry, Palacky University, 77146 Olomouc, Listopadu 12, Czech Republic |
| Abstract: | 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. |
| Keywords: | Riemannian manifold Differential forms Elliptic second order linear differential operators on differential forms Betti numbers Tachibana numbers |
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