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Special multiply Einstein warped products with an affine connection

Faculty of Engineering, Computer Science and Geography, Spiru Haret University of Bucharest, 46B Fabricii Str, Bucharest, Romania

E-mail Address: dandumitru2011@gmail.com

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https://doi.org/10.1142/S0219887818501074Cited by:2 (Source: Crossref)

Abstract

The aim of this paper is to study special multiply Einstein warped products having an affine connection. Let $M = I \times_{f_{1}} F_{1} \times \dots \times_{f_{m}} F_{m}$ be a multiply warped product such that $I \subset ℝ$ is an open interval, $dim I = 1,$ $f_{i} : I \to (0, \infty),$ $f_{i} \in 𝒞^{\infty} (I),$ $dim F_{i} = k_{i} \geq 1$ for every $i \in {1, \dots, m},$ $m \geq 1,$ $dim M = \bar{n} = 1 + \sum_{i = 1}^{m} k_{i}$ and $\bar{\nabla}$ an affine connection on $M .$ We compute the warping functions that make $M$ an Einstein space in the following cases:

^(a)	$\bar{\nabla}$ is a semi-symmetric metric/non-metric connection and all the fibers are Ricci flat.
^(b)	$\bar{\nabla}$ is a quarter-symmetric metric/non-metric connection and all the fibers are Ricci flat.

Keywords:

AMSC: 53C25, 53C50

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