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C. Bejan, O. Kowalski (2015)
On some differential operators on natural Riemann extensionsAnnals of Global Analysis and Geometry, 48
O. Kowalski, Masami Sekizawa (2016)
Existence and classification of three-dimensional Lorentzian manifolds with prescribed distinct Ricci eigenvaluesJournal of Geometry and Physics, 99
M. Dunajski, T. Mettler (2015)
Gauge Theory on Projective Surfaces and Anti-self-dual Einstein Metrics in Dimension FourJournal of Geometric Analysis, 28
P. Girard (1999)
Einstein’s equations and Clifford algebraAdvances in Applied Clifford Algebras, 9
O. Kowalski, Masami Sekizawa (2011)
On natural Riemann extensionsPublicationes Mathematicae Debrecen, 78
M. Brozos-V'azquez, E. Garc'ia-R'io (2014)
Four-dimensional neutral signature self-dual gradient Ricci solitonsarXiv: Differential Geometry
G. Hall, B. Kırık (2015)
Recurrence structures in 4-dimensional manifolds with metric of signature (+,+,−,−)(+,+,−,−)Journal of Geometry and Physics, 98
M. Dunajski, P. Tod (2009)
Four–dimensional metrics conformal to KählerMathematical Proceedings of the Cambridge Philosophical Society, 148
Masami Sekizawa (1987)
Natural transformations of affine connections on manifolds to metrics on cotangent bundles
I. Burdujan (2003)
On almost Cliffordian manifoldsItalian journal of pure and applied mathematics
Andrei Moroianu, U. Semmelmann (2009)
CLIFFORD STRUCTURES ON RIEMANNIAN MANIFOLDSAdvances in Mathematics, 228
K. Yano, E. Patterson (1967)
Vertical and complete lifts from a manifold to its cotangent bundleJournal of The Mathematical Society of Japan, 19
T. Willmore (1975)
TANGENT AND COTANGENT BUNDLESBulletin of The London Mathematical Society, 7
J. Robbin, Uw Madison, D. Salamon (2011)
INTRODUCTION TO DIFFERENTIAL GEOMETRY
(2008)
Einstein manifolds
M. Crasmareanu, L. Piscoran (2016)
Weak Para-CR Structures on Vertical BundlesAdvances in Applied Clifford Algebras, 26
I. Burdujan (2008)
Clifford-Kähler manifolds
EM Patterson, AG Walker (1952)
Riemannian extensionsQ. J. Math. Oxford Ser., 2
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.
Advances in Applied Clifford Algebras – Springer Journals
Published: Mar 21, 2017
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