## Abstract

The tensor R · C − C · R and the tensors Q(g, R), Q(S, R), Q(g, C) and Q(S, C) of every Einstein manifold (M, g), n ≥ 4, satisfy R · C − C · R = (κ/((n − 1)n)) Q(g, R) = (κ/((n − 1)n)) Q(g, C) = (1/(n − 1)) Q(S, R) = (1/(n − 1)) Q(S, C). Motivated by this we study curvature properties of non-Einstein and non-conformally flat semi-Riemannian manifolds of dimension ≥ 4 satisfying the following family of generalized Einstein metric conditions: the tensor R· C − C · R is a linear combination of the tensors Q(g, R), Q(S, R), Q(g, C), Q(S, C), Q(g, g ∧ S ) and Q(S, g ∧ S ). We present results on quasi-Einstein and 2-quasi-Einstein warped product manifolds satisfying particular conditions of these family of conditions.

Original language | English |
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Title of host publication | 5th International Conference of Mathematical Sciences, ICMS 2021 |

Editors | Huseyin Cakalli, Ljubisa D. R. Kocinac, Allaberen Ashyralyev, Robin Harte, Mehmet Dik, Ibrahim Canak, Hacer Sengul Kandemir, Mujgan Tez, Ozay Gurtug, Ekrem Savas, Nazlim Deniz Aral, Filiz Cagatay Ucgan, Onder Sahinaslan, Charyyar Ashyralyyev, Sefa Anil Sezer, Arap Duran Turkoglu, Oruc Raif Onvural, Hakan Sahin |

Publisher | American Institute of Physics Inc. |

ISBN (Electronic) | 9780735442580 |

DOIs | |

Publication status | Published - 7 Nov 2022 |

Event | 5th International Conference of Mathematical Sciences, ICMS 2021 - Istanbul, Turkey Duration: 23 Jun 2021 → 27 Jun 2021 |

### Publication series

Name | AIP Conference Proceedings |
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Volume | 2483 |

ISSN (Print) | 0094-243X |

ISSN (Electronic) | 1551-7616 |

### Conference

Conference | 5th International Conference of Mathematical Sciences, ICMS 2021 |
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Country/Territory | Turkey |

City | Istanbul |

Period | 23/06/21 → 27/06/21 |

### Bibliographical note

Publisher Copyright:© 2022 American Institute of Physics Inc.. All rights reserved.

## Keywords

- 2-quasi-Einstein manifold
- Einstein manifold
- generalized Einstein metric condition
- pseudosymmetry type curvature condition
- quasi-Einstein manifold
- warped product manifold