Vanishing theorems for higher-order Killing and Codazzi
A Killing p-tensor (for an arbitrary natural number p ≥ 2) is a symmetric p-tensor with vanishing symmetrized covariant derivative. On the other hand, Codazzi p-tensor is a symmetric p-tensor with symmetric covariant derivative. Let M be a complete and simply connected Riemannian manifold of nonp...
| Published in: | Дифференциальная геометрия многообразий фигур |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Immanuel Kant Baltic Federal University
2019-08-01
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| Subjects: | |
| Online Access: | https://journals.kantiana.ru/geometry/4279/12677/ |
| Summary: | A Killing p-tensor (for an arbitrary natural number p ≥ 2) is a symmetric p-tensor with vanishing symmetrized covariant derivative. On the other hand, Codazzi p-tensor is a symmetric p-tensor with symmetric covariant derivative. Let M be a complete and simply connected Riemannian manifold of nonpositive (resp. non-negative) sectional curvature. In the first case we prove that an arbitrary symmetric traceless Killing p-tensor is parallel on M if its norm is a -function for some q > 0. If in addition the volume of this manifold is infinite, then this tensor is equal to zero. In the second case we prove that an arbitrary traceless Codazzi p-tensor is equal to zero on a noncompact manifold M if its norm is a -function for some .
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| ISSN: | 0321-4796 2782-3229 |