Derivatives of the Lie structure operator on a real hypersurface in complex projective space
| Autor: | Juan de Dios Pérez, David Pérez-López |
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| Rok vydání: | 2021 |
| Předmět: |
Physics
010505 oceanography General Mathematics Complex projective space 010102 general mathematics Type (model theory) 01 natural sciences Tensor field Combinatorics Hypersurface Skew-symmetric matrix Lie derivative 0101 mathematics Connection (algebraic framework) 0105 earth and related environmental sciences Real number |
| Zdroj: | Monatshefte für Mathematik. 196:281-303 |
| ISSN: | 1436-5081 0026-9255 |
| DOI: | 10.1007/s00605-021-01586-w |
| Popis: | If we consider a real hypersurface M in a complex projective space we have the covariant derivatives associated to both the Levi-Civita connection and, for any nonnull real number k, to the k-th generalized Tanaka-Webster connection. We also have the Lie derivative and a derivative of Lie type associated to the k-th generalized Tanaka-Webster connection. If we consider the structure Lie operator $$L_{\xi }$$ on M, we can define two tensor fields of type (1,2) on M from $$L_{\xi }$$ associated to the derivatives mentioned above, $$L_{{\xi }_F}^{(k)}$$ and $$L_{{\xi }_T}^{(k)}$$ . Kaimakamis, Panagiotidou and Perez obtained the classifications of real hypersurfaces for which either $$L_{{\xi }_F}^{(k)}$$ or $$L_{{\xi }_T}^{(k)}$$ identically vanish. We generalize such results classifying real hypersurfaces in complex projective space such that $$L_{{\xi }_F}^{(k)}$$ (respectively, $$L_{{\xi }_T}^{(k)}$$ ) is either symmetric or skew symmetric. |
| Databáze: | OpenAIRE |
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