### On Perelman’s functional with curvature corrections

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

Caianiello, E. R., Feoli, A., Gasperini, M., Scarpetta G., Quantum corrections to the spacetime metric from geometric phase space quantization, Int. J. Theor. Phys. 29 (2) (1990), 131-139.

Cao, H.-D, Existence of gradient Kahler–Ricci solitons, Elliptic and Parabolic Methods in Geometry (Minneapolis, 1994), 1-16, A. K. Peters, Wellesley MA, 1996.

Cao, H.-D., Zhu, X.-P., A complete proof of the Poincare and Geometrization conjectures - application of the Hamilton-Perelman theory of the Ricci flow, Asian J. Math., 10, no. 2 (2006), 165-492.

Calcagni, G., Geometry and field theory in multi-fractional spacetime, JHEP01 (2012) 065, 61 pp.

D’Hoker, E., String Theory, in Quantum Fields and Strings: A Course for Mathematicians, vol. 2, American Mathematical Society, Providence, 1999.

Davis, S., Luckock, H., The effect of higher-order curvature terms on string quantum cosmology, Phys. Lett. B 485 (2000), 408-421.

Dowker, H. F., Topology change in quantum gravity, The Future of Theoretical Physics and Cosmology, eds. G. W. Gibbons, S. J. Rankin, E. P. S. Shellard, Cambridge Univ. Press, (2003), p. 879.

Dzhunushaliev, V., Quantum wormhole as a Ricci flow, Int. J. Geom. Meth. Mod. Phys. 6 (2009), 1033-1046.

Dzhunushaliev, V., Serikbayev, N., Myrzakulov, R., Topology change in quantum gravity and Ricci flows, arXiv:0912.5326v2.

El-Nabulsi, R. A., Fractional field theories from multidimensional fractional variational problems, Int. J. Mod. Geom. Meth. Mod. Phys. 5, no. 6 (2008), 863-892.

El-Nabulsi, R. A., Complexified quantum field theory and mass without mass from multidimensional fractional actionlike variational approach with time-dependent fractional exponent, Chaos, Solitons Fractals 42, no. 4 (2009), 2384-2398.

El-Nabulsi, R. A., Fractional quantum field theory on multifractal sets, American. J. Eng. Appl. Sci. 4 (1) (2010), 133-141.

El-Nabulsi, R. A., Modifications at large distance from fractional and fractal arguments, Fractals 18, no. 2 (2010), 185-190.

El-Nabulsi, R. A., Glaeske-Kilbas-Saigo fractional integration and fractional Dixmier trace, Acta Math. Viet. 37, no. 2 (2012), 149-160.

El-Nabulsi, R. A, Wu, G.-C., Fractional complexified field theory from Saxena–Kumbhat fractional integral, fractional derivative of order and dynamical fractional integral exponent, Afric. Disp. J. Math. 13, no. 2 (2012), 45-61.

Gibbons, G. W., Topology change in classical and quantum gravity, Published in Mt. Sorak Symposium 1991: 159-185 (QCD161:S939:1991) Developments in Field Theory, ed. Jihn E Kim (Min Eum Sa, Seoul) (1992); arXiv:1110.0611v1.

Gibbons, G.W., Hawking, S. W., Action integrals and partition functions in quantum gravity, Phys. Rev. D 15 (1977), 2752-2756.

Goldfain, E., Fractional dynamics and the standard model for particle physics, Comm. Nonlinear Sci. Numer. Simul. 13 (2008), 1397-1404.

Hamilton, R., Three manifolds with positive Ricci curvature, Jour. Diff. Geom. 17 (1982), 255-306.

Hamilton, R., Four-manifolds with positive curvature operator, J. Diff. Geom. 24 (2) (1986), 153-179.

Hamilton, R., Formation of singularities in the Ricci flow, Surveys in Diff. Geom. 2 (1997), 7-136.

Headrick, M., Wiseman, T., Ricci flow and black holes, Class. Quant. Grav. 23 (2006), 6683-6708.

Herrmann, R., Gauge invariance in fractional field theories, Phys. Lett. A 372 (2008), 5515-5522.

Jolany, H., Perelman’s functional and reduced volume, arXiv:1004.1785.

Mohaupt, T., Strings, higher curvature corrections, and black holes, talk given at the 2nd Workshop on Mathematical and Physical Aspects of Quantum Gravity, Blaubeuren, 28 July-1 August, (2005); hep-th/0512048.

Perelman, G., Finite extinction time for the solutions to the Ricci flow on certain three manifolds, math.DG/0307245v1.

Perelman, G., Ricci flow with surgery on three-manifolds, math.DG/0303109v1.

Perelman, G., The entropy formula for the Ricci flow and its geometric applications, http://arXiv.org/abs/math.DG/0211159.

Thurston, William P., Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, American Mathematical Society. Bulletin. New Series 6 (3) (1982), 357-381.

Vacaru, S., Spectral functionals, nonholonomic Dirac operators, and noncommutative Ricci flows, J. Math. Phys. 50 (2009), 073503, 24 pp.

Vacaru, S., Fractional dynamics from Einstein gravity, general solutions, and black holes, Int. J. Theor. Phys. 51 (2012), 1338-1359.

Vacaru, S., Fractional nonholonomic Ricci flows, Chaos, Solitons and Fractals 45 (2012), 1266-1276.

Vacaru, S., Nonholonomic Clifford and Finsler structures, non-commutative Ricci flows, and mathematical relativity, arXiv: 1205.5387.

DOI: http://dx.doi.org/10.17951/a.2012.66.2.47-55

Data publikacji: 2016-07-25 12:22:16

Data złożenia artykułu: 2016-07-25 11:27:14

### Refbacks

- There are currently no refbacks.

Copyright (c) 2012 Rami Ahmad El-Nabulsi