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
References
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.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.