On the Tachibana numbers of closed manifolds with pinched negative sectional curvature
Conformal Killing form is a natural generalization of conformal Killing vector field. These forms were extensively studied by many geometricians. These considerations were motivated by existence of various applications for these forms. The vector space of conformal Killing p-forms on an n-dimen...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Immanuel Kant Baltic Federal University
2020-08-01
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| Series: | Дифференциальная геометрия многообразий фигур |
| Subjects: | |
| Online Access: | https://journals.kantiana.ru/geometry/4686/25784/ |
| _version_ | 1811272562864291840 |
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| author | S.E. Stepanov I. I. Tsyganok |
| author_facet | S.E. Stepanov I. I. Tsyganok |
| author_sort | S.E. Stepanov |
| collection | DOAJ |
| description | Conformal Killing form is a natural generalization of conformal Killing vector field. These forms were extensively studied by many geometricians. These considerations were motivated by existence of various applications for these forms. The vector space of conformal Killing p-forms on an n-dimensional closed Riemannian manifold M has a finite dimension named the Tachibana number. These numbers are conformal scalar invariant of M and satisfy the duality theorem: . In the present article we prove two vanishing theorems. According to the first theorem, there are no nonzero Tachibana numbers on an n-dimensional closed Riemannian manifold with pinched negative sectional curvature such that for some pinching constant . From the second theorem we conclude that there are no nonzero Tachibana numbers on a three-dimensional closed Riemannian manifold with negative sectional curvature.
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| first_indexed | 2024-04-12T22:41:22Z |
| format | Article |
| id | doaj.art-5ee4be6531ed4b659654be99d7f3d1ba |
| institution | Directory Open Access Journal |
| issn | 0321-4796 2782-3229 |
| language | English |
| last_indexed | 2024-04-12T22:41:22Z |
| publishDate | 2020-08-01 |
| publisher | Immanuel Kant Baltic Federal University |
| record_format | Article |
| series | Дифференциальная геометрия многообразий фигур |
| spelling | doaj.art-5ee4be6531ed4b659654be99d7f3d1ba2022-12-22T03:13:41ZengImmanuel Kant Baltic Federal UniversityДифференциальная геометрия многообразий фигур0321-47962782-32292020-08-015111612210.5922/0321-4796-2020-51-13On the Tachibana numbers of closed manifolds with pinched negative sectional curvatureS.E. Stepanov0https://orcid.org/0000-0003-1734-8874I. I. Tsyganok1https://orcid.org/0000-0001-9186-3992Financial University under the Government of the Russian FederationFinancial University under the Government of the Russian FederationConformal Killing form is a natural generalization of conformal Killing vector field. These forms were extensively studied by many geometricians. These considerations were motivated by existence of various applications for these forms. The vector space of conformal Killing p-forms on an n-dimensional closed Riemannian manifold M has a finite dimension named the Tachibana number. These numbers are conformal scalar invariant of M and satisfy the duality theorem: . In the present article we prove two vanishing theorems. According to the first theorem, there are no nonzero Tachibana numbers on an n-dimensional closed Riemannian manifold with pinched negative sectional curvature such that for some pinching constant . From the second theorem we conclude that there are no nonzero Tachibana numbers on a three-dimensional closed Riemannian manifold with negative sectional curvature. https://journals.kantiana.ru/geometry/4686/25784/riemannian manifoldconformal killing — yano tensorsectional curvaturevanishing theorem |
| spellingShingle | S.E. Stepanov I. I. Tsyganok On the Tachibana numbers of closed manifolds with pinched negative sectional curvature Дифференциальная геометрия многообразий фигур riemannian manifold conformal killing — yano tensor sectional curvature vanishing theorem |
| title | On the Tachibana numbers of closed manifolds with pinched negative sectional curvature |
| title_full | On the Tachibana numbers of closed manifolds with pinched negative sectional curvature |
| title_fullStr | On the Tachibana numbers of closed manifolds with pinched negative sectional curvature |
| title_full_unstemmed | On the Tachibana numbers of closed manifolds with pinched negative sectional curvature |
| title_short | On the Tachibana numbers of closed manifolds with pinched negative sectional curvature |
| title_sort | on the tachibana numbers of closed manifolds with pinched negative sectional curvature |
| topic | riemannian manifold conformal killing — yano tensor sectional curvature vanishing theorem |
| url | https://journals.kantiana.ru/geometry/4686/25784/ |
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