Fractional nonholonomic Ricci flows |
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| Authors: | Sergiu I Vacaru |
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| Institution: | 1. Humboldt University, 10099 Berlin, Germany;2. Radboud University Nijmegen, 6525 AJ Nijmegen, The Netherlands;1. Key Laboratory of Seismic Observation and Geophysical Imaging, Institute of Geophysics, China Earthquake Administration, Beijing 100081, China;2. State Key Laboratory of Earthquake Dynamics, Institute of Geology, China Earthquake Administration, Beijing 100029, China;1. University of Zielona Góra, ul. Podgórna 50, 65-246 Zielona Góra, Poland;2. School of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, UK;3. Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, ul. Grudziadzka 5, 87-100 Torun, Poland;1. Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India;2. Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada;3. Department of Physics, Faculty of Sciences, Benha University, Benha 13518, Egypt |
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| Abstract: | We formulate the fractional Ricci flow theory for (pseudo) Riemannian geometries enabled with nonholonomic distributions defining fractional integro-differential structures, for non-integer dimensions. There are constructed fractional analogs of Perelman’s functionals and derived the corresponding fractional evolution (Hamilton’s) equations. We apply in fractional calculus the nonlinear connection formalism originally elaborated in Finsler geometry and generalizations and recently applied to classical and quantum gravity theories. There are also analyzed the fractional operators for the entropy and fundamental thermodynamic values. |
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