1. 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)

2. 1. A specification of a Bourguignon’s result

5. 2. Harmonic and conformal Killing r-forms

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

8. 3. A rough Laplacian on differential forms

10. 4. The Tachibana numbers and their properties

13. 5. Curvature and Tachibana numbers

17. 7. Some relationships between the Tachibana numbers and Betti numbers

18. 6. Some relationships between the Tachibana numbers and Betti numbers

21. 7. The existence of the Betti numbers

22. 8. The existence of the Betti numbers

23. Thank you for your attention!