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The Tachibana numbers of a compact Riemannian manifold Sergey E. Stepanov Dept. of Math., Finance University under the Government of Russian Federation, Moscow (Russia) Josef Mikeš Dept. of Algebra and Geometry, Palanky University, Olomouc (Czech Republic)

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1. A specification of a Bourguignon’s result

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2. Harmonic and conformal Killing r-forms

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A 3D-diagram of the classification of differential r-forms

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3. A rough Laplacian on differential forms

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4. The Tachibana numbers and their properties

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5. Curvature and Tachibana numbers

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7. Some relationships between the Tachibana numbers and Betti numbers

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6. Some relationships between the Tachibana numbers and Betti numbers

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7. The existence of the Betti numbers

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8. The existence of the Betti numbers

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Thank you for your attention!

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