Results 41 to 50 of about 727 (144)

Metric flows with neural networks

Machine Learning: Science and Technology
We develop a general theory of flows in the space of Riemannian metrics induced by neural network (NN) gradient descent. This is motivated in part by recent advances in approximating Calabi–Yau metrics with NNs and is enabled by recent advances in ...
James Halverson, Fabian Ruehle
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Curvature and Solitonic Structures of Para-Sasakian Manifolds With Schouten–van Kampen Connection on the Tangent Bundle

Journal of Mathematics
This paper investigates the complete lift of para-Sasakian structures to the tangent bundle equipped with the Schouten–van Kampen connection (SVKC). By analyzing curvature tensors and soliton equations, we establish the existence of Ricci, Yamabe, and η ...
Lalnunenga Colney, Dalal Alhwikem, Teg Alam   +2 more
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Generalized Ricci Flow

, 2020
This book gives an introduction to fundamental aspects of generalized Riemannian, complex, and K hler geometry. This leads to an extension of the classical Einstein-Hilbert action, which yields natural extensions of Einstein and Calabi-Yau structures as `canonical metrics' in generalized Riemannian and complex geometry.
Garcia-Fernandez, Mario, Streets, Jeffrey   +1 more
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On non-degenerate singular points of normalized Ricci flows on some generalized Wallach spaces

Қарағанды университетінің хабаршысы. Математика сериясы, 2015
The present paper devoted to problems of Riemannian geometry and planar dynamical systems. In particular we study nondegenerate singular points of normalized Ricci flows on special type of generalized Wallach spaces.
N.А. Аbiev, Z.O. Turtkulbayeva
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Ricci Flow and Volume Renormalizability [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2019
With respect to any special boundary defining function, a conformally compact asymptotically hyperbolic metric has an asymptotic expansion near its conformal infinity. If this expansion is even to a certain order and satisfies one extra condition, then it is possible to define its renormalized volume and show that it is independent of choices that ...
Bahuaud, E., Mazzeo, R., Woolgar, E.
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Geometric and Structural Properties of Indefinite Kenmotsu Manifolds Admitting Eta-Ricci–Bourguignon Solitons

Mathematics
This paper undertakes a detailed study of η-Ricci–Bourguignon solitons on ϵ-Kenmotsu manifolds, with particular focus on three special types of Ricci tensors: Codazzi-type, cyclic parallel and cyclic η-recurrent tensors that support such solitonic ...
Md Aquib, Oğuzhan Bahadır, Laltluangkima Chawngthu, Rajesh Kumar   +3 more
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Convergence Stability for Ricci Flow [PDF]

The Journal of Geometric Analysis, 2019
18 ...
Eric Bahuaud, Christine Guenther, James Isenberg   +2 more
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Navigating string theory field space with geometric flows

Journal of High Energy Physics
The Swampland Distance Conjecture postulates the emergence of an infinite tower of massless states when approaching infinite-distance points in moduli space.
Saskia Demulder, Dieter Lüst, Thomas Raml   +2 more
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POSITIVITY OF RICCI CURVATURE UNDER THE KÄHLER–RICCI FLOW [PDF]

Communications in Contemporary Mathematics, 2006
In each complex dimension n ≥ 2, we construct complete Kähler manifolds of bounded curvature and non-negative Ricci curvature whose Kähler–Ricci evolutions immediately acquire Ricci curvature of mixed sign.
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Eigenvalue lower bounds and splitting for modified Ricci flow

Advanced Nonlinear Studies
We prove sharp lower bounds for eigenvalues of the drift Laplacian for a modified Ricci flow. The modified Ricci flow is a system of coupled equations for a metric and weighted volume that plays an important role in Ricci flow.
Colding Tobias Holck, Minicozzi II William P.   +1 more
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