# Einstein Metrics Induced by Natural Riemann Extensions

Einstein Metrics Induced by Natural Riemann Extensions Clifford algebras are used in theoretical physics and in particular, in the general theory of relativity, where Einstein’s equations are rewritten in Girard (Adv Appl Clifford Algebras 9(2):225–230, 1999) within a Clifford algebra. Let M be a manifold with a torsion-free connection which induces on its cotangent bundle $$T^{*}M$$ T ∗ M , a semi-Riemannian metric $$\bar{g}$$ g ¯ , called the natural Riemann extension, Kowalski and Sekizawa (Publ Math Debrecen 78:709–721, 2011). The main result of the present paper gives a necessary and sufficient condition for $$\bar{g}$$ g ¯ restricted to certain hypersurfaces of $$T^{*}M$$ T ∗ M to be Einstein. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Applied Clifford Algebras Springer Journals

# Einstein Metrics Induced by Natural Riemann Extensions

, Volume 27 (3) – Mar 21, 2017
11 pages

/lp/springer_journal/einstein-metrics-induced-by-natural-riemann-extensions-RjSkKgYjGV
Publisher
Springer International Publishing
Subject
Physics; Mathematical Methods in Physics; Theoretical, Mathematical and Computational Physics; Applications of Mathematics; Physics, general
ISSN
0188-7009
eISSN
1661-4909
D.O.I.
10.1007/s00006-017-0774-2
Publisher site
See Article on Publisher Site

### Abstract

Clifford algebras are used in theoretical physics and in particular, in the general theory of relativity, where Einstein’s equations are rewritten in Girard (Adv Appl Clifford Algebras 9(2):225–230, 1999) within a Clifford algebra. Let M be a manifold with a torsion-free connection which induces on its cotangent bundle $$T^{*}M$$ T ∗ M , a semi-Riemannian metric $$\bar{g}$$ g ¯ , called the natural Riemann extension, Kowalski and Sekizawa (Publ Math Debrecen 78:709–721, 2011). The main result of the present paper gives a necessary and sufficient condition for $$\bar{g}$$ g ¯ restricted to certain hypersurfaces of $$T^{*}M$$ T ∗ M to be Einstein.

### Journal

Advances in Applied Clifford AlgebrasSpringer Journals

Published: Mar 21, 2017

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