SPLITTING THEOREMS IN PRESENCE OF AN IRROTATIONAL VECTOR FIELD
作者： Benjamin Olea , Manuel Gutierrez
DOI:
关键词: Complex lamellar vector field 、 Curl (mathematics) 、 Conservative vector field 、 Solenoidal vector field 、 Vector potential 、 Invariant manifold 、 Mathematics 、 Fundamental vector field 、 Mathematical analysis 、 Congruence (general relativity)
摘要: New splitting theorems in a semi-Riemannian manifold which ad- mits an irrotational vector field (not necessarily gradient) with some suitable properties are obtained. According to the extras hypothesis assumed on field, we can get twisted, warped or direct decompositions. Some appli- cations Lorentzian shown and also S 1 × L type decomposition is treated.
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Miguel Sánchez, On the Geometry of Generalized Robertson± Walker Spacetimes: Geodesics General Relativity and Gravitation. ,vol. 30, pp. 915- 932 ,(1998) , 10.1023/A:1026664209847
Nobuhiro Innami, Splitting theorems of riemannian manifolds Compositio Mathematica. ,vol. 47, pp. 237- 247 ,(1982)
Barrett O'Neill, Semi-Riemannian Geometry With Applications to Relativity ,(2011)
Gilbert Hector, Ulrich Hirsch Galdós, Introduction to the geometry of foliations F. Vieweg & Sohn. ,(1986)
Eduardo García-Río, Demir N. Kupeli, Some Splitting Theorems for Stably Causal Spacetimes General Relativity and Gravitation. ,vol. 30, pp. 35- 44 ,(1998) , 10.1023/A:1018816815433
H. Wu, On the de Rham decomposition theorem Illinois Journal of Mathematics. ,vol. 8, pp. 291- 311 ,(1964) , 10.1215/IJM/1256059674
Gerard Walschap, Spacelike metric foliations Journal of Geometry and Physics. ,vol. 32, pp. 97- 101 ,(1999) , 10.1016/S0393-0440(99)00021-2
Richard S. Palais, A Global Formulation of the Lie Theory of Transformation Groups ,(1957)
Arthur E. Fischer, Riemannian submersions and the regular interval theorem of Morse theory Annals of Global Analysis and Geometry. ,vol. 14, pp. 263- 300 ,(1996) , 10.1007/BF00054474
Steven G. Harris, A characterization of Robertson-Walker spaces by null sectional curvature General Relativity and Gravitation. ,vol. 17, pp. 493- 498 ,(1985) , 10.1007/BF00761906