Bejan, Cornelia-LiviaMeric, Semsi EkenKilic, Erol2024-08-042024-08-0420170188-70091661-4909https://doi.org/10.1007/s00006-017-0774-2https://hdl.handle.net/11616/97738Clifford 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 , a semi-Riemannian metric (g) over bar , 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 (g) over bar restricted to certain hypersurfaces of T* M to be Einstein.eninfo:eu-repo/semantics/closedAccessClifford algebraCotangent BundleEinstein manifoldNatural Riemann ExtensionArticle2732333234310.1007/s00006-017-0774-22-s2.0-85015789759Q3WOS:000408268200023Q2