Einstein Metrics Induced by Natural Riemann Extensions

BEJAN C., Meric S. E. , KILIÇ E.

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, cilt.27, ss.2333-2343, 2017 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 27 Konu: 3
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1007/s00006-017-0774-2
  • Dergi Adı: ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • Sayfa Sayıları: ss.2333-2343

Özet

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 , 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.