A. Gray presented an interesting O(n) invariant decomposition of the covariant derivative of the Ricci tensor. Manifolds whose Ricci tensor satisfies the defining property of each orthogonal class are called Einstein-like manifolds. In the present paper, we answered the following question: Under what condition(s), does a factor manifold M-i, i = 1, 2 of a doubly warped product manifold M = (f2) M-1 x (f1) M-2 lie in the same Einstein-like class of M? By imposing sufficient and necessary conditions on the warping functions, an inheritance property of each class is proved. As an application, Einstein-like doubly warped product space-times of type A, B or P are considered.

Gray’s decomposition on doubly warped product manifolds and applications / H. El-Sayied, C. Mantica, S. Shenawy, N. Syied. - In: FILOMAT. - ISSN 0354-5180. - 34:11(2020), pp. 3767-3776. [10.2298/FIL2011767E]

Gray’s decomposition on doubly warped product manifolds and applications

C. Mantica
Secondo
;
2020

Abstract

A. Gray presented an interesting O(n) invariant decomposition of the covariant derivative of the Ricci tensor. Manifolds whose Ricci tensor satisfies the defining property of each orthogonal class are called Einstein-like manifolds. In the present paper, we answered the following question: Under what condition(s), does a factor manifold M-i, i = 1, 2 of a doubly warped product manifold M = (f2) M-1 x (f1) M-2 lie in the same Einstein-like class of M? By imposing sufficient and necessary conditions on the warping functions, an inheritance property of each class is proved. As an application, Einstein-like doubly warped product space-times of type A, B or P are considered.
Codazzi Ricci tensor; doubly warped manifolds; Killing Ricci tensor; doubly warped space-times; Einstein-like manifolds;
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
Settore MAT/03 - Geometria
2020
Article (author)
File in questo prodotto:
File Dimensione Formato  
0354-51802011767E.pdf

accesso aperto

Tipologia: Publisher's version/PDF
Dimensione 223.51 kB
Formato Adobe PDF
223.51 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/1019937
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 8
  • ???jsp.display-item.citation.isi??? 6
social impact