Dissipative Hyperbolic Geometric Flowon Modified Riemann Extensions
DOI:
https://doi.org/10.26713/cma.v6i2.311Keywords:
Dissipative hyperbolic flow, Modified Riemann extension, Evolution equationsAbstract
We study the properties of modified Riemann extensions evolving under dissipative hyperbolic geometric flow with examples.Downloads
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E. Calvino-Louzao et al., The geometry of modified Riemannian extensions, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 465 (2107) (2009), 2023–2040.
E. Calvino-Louzao, E. García-Río and R. Vázquez-Lorenzo, Riemann extensions of torsion-free connections with degenerate Ricci tensor, Canad. J. Math. 62 (5) (2010), 1037–1057.
W.-R. Dai, D.-X. Kong and K. Liu, Dissipative hyperbolic geometric flow, Asian J. Math. 12 (3) (2008), 345–364.
W.-R. Dai, D.-X. Kong and K. Liu, Hyperbolic geometric flow (I): short-time existence and nonlinear stability, Pure Appl. Math. Q. 6 (2) (2010), Special Issue: In honor of Michael Atiyah and Isadore
Singer, 331–359.
V.S. Dryuma, Teoret. Mat. Fiz. 146 (1) (2006), 42–54; translation in Theoret. and Math. Phys. 146 (1) (2006), 34–44.
L.P. Eisenhart, Fields of parallel vectors in Riemannian space, Ann. of Math. 39 (2) (1938), 316–321.
A. Gezer, L. Bilen and A. Cakmak, Properties of modified Riemannian extensions, arXiv:1305. 4478v2 [math.DG] 26 May 2013.
D.-X. Kong and K. Liu, Wave character of metrics and hyperbolic geometric flow, J. Math. Phys. 48 (10) (2007), 103508, 14 p.
O. Kowalski and M. Sekizawa, The Riemann extensions with cyclic parallel Ricci tensor, Math. Nachr. 287 (8-9) (2014), 955–961.
W. Lu, Evolution equations of curvature tensors along the hyperbolic geometric flow, Chin. Ann. Math. Ser. B 35 (6) (2014), 955–968.
E.M. Patterson and A.G. Walker, Riemann extensions, Quart. J. Math., Oxford Ser. 3 (2) (1952), 19–28.
A.G. Walker, Canonical form for a Riemannian space with a parallel field of null planes, Quart. J. Math., Oxford Ser. 1 (2) (1950), 69–79.
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