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Showing 1 to 14 of 14 for “"Ricci Curvature"”.
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Ricci Curvature of Finsler Metrics by Warped Product
… characterization for the proposed metrics to be Ricci-flat and construct explicit examples. Whenever possible, we describe both positive-definite solutions and solutions with Lorentz signature. For the latter, the 4-dimensional metrics may also be studied as Finsler spacetimes.
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N-Bakry Emery Ricci Curvature & N-Quasi Einstein Metrics
… We then give a semi-intuitive description on Ricci curvature for the non-geometer. We give a description of the N-Bakry- Émery Ricci curvature and the N-quasi Einstein metric. The main results in this thesis are related to the N-Bakry-Émery Ricci curvature and the N-quasi Einstein metric.</p> …
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N-bakry Emery Ricci Curvature & N-quasi Einstein Metrics
… We then give a semi-intuitive description on Ricci curvature for the non-geometer. We give a description of the N-Bakry- Émery Ricci curvature and the N-quasi Einstein metric. The main results in this thesis are related to the N-Bakry-Émery Ricci curvature and the N-quasi Einstein …
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Ricci Curvature of Noncommutative Three Tori, Entropy, and Second Quantization
… define suitable notions such as volume, scalar curvature, and Ricci curvature. In particular, one can construct the Ricci curvature from the asymptotic expansion of the heat trace $textrm{Tr}(e^{-tD^2})$. In Chapter 2, we will compute the Ricci curvature of a curved noncommutative three torus. …
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Geometry and analysis of Ricci curvature and mean curvature flows
… study the geometry and analysis of spaces with Ricci curvature bounded below from the following three perspectives and the asymptotically conical singularities of mean curvature flows in the following two perspectives. For the spaces with Ricci curvature bounded below, firstly we study the …
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Positive Sasakian Structures on Links of Weighted Complete Intersection Singularities
… known that Sasaki-Einstein metrics have positive Ricci curvature, and since positive Sasakian structures give rise to Sasakian metrics with positive Ricci curvature, it is useful to determine which links have a positive Sasakian structure. This corresponds to the Fano index of the associated …
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Interpolation of Weighted L2 Holomorphic Functions in Higher Dimensions
… a Kahler manifold X with a metric &ohgr; whose Ricci curvature is non-positive and we assume that X admits a Green's function. In this setup we give a sufficient condition for a closed smooth uniformly flat hypersurface W in X to be interpolating. Our condition is expressed in terms of a …
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Functional inequalities and the curvature dimension inequality on totally geodesic foliations
… totally geodesic foliations. Under a certain curvature condition, we obtain (1) Sobolev-isoperimetric inequalities, global Poincar\'e inqualities, and a lower bound for Cheeger's isoperimetric constant, (2) Poincar\'e inequalities on balls and uniqueness of positive(or $L^p,p\geq 1$) solutions …
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CLASSIFICATION RESULTS FOR SEMILINEAR ELLIPTIC EQUATIONS
… presence on the underlying manifold. When the Ricci curvature is non-negative, we prove both the classification of positive solutions to the critical equation and the rigidity for the ambient manifold. The same results are obtained when we consider solutions to the Liouville equation on …
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Limiting behavior of Ricci flows
Consider the unnormalized Ricci flow ...Richard Hamilton showed that if the curvature operator is uniformly bounded under the flow for all times ... then the solution can be extended beyond T. In the thesis we prove that if the Ricci curvature is uniformly bounded under the flow for all times ... …
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A minimization of a curvature functional on fiber bundles
… metric on the base, $g\sb{f}$ is a constant curvature metric on the fiber invariant under the action of the group. We can obtain a new metric on M by scaling the horizontal component of the original by $e\sp{2u}$ and the vertical component by $f\sp2,$ where u and f are smooth functions on the …
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Vignettes in string theory : using geometry to probe the worldsheet and strongly coupled physics
… case, the beta function is proportional to the Ricci curvature so that conformal invariance demands Ricci-flatness. We extend this analysis to the case where space and time derivatives come with different target space metrics. We also speculate about coupling the theory to gravity. Finally, we …
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Cosmological dynamics of exponential gravity
… and only become effective at late times when the Ricci curvature R decreases. In our discussion we indicate how these corrections can be interpreted as an effective fluid of purely geometrical origin; we also discuss the phase space and stability of deSitter space in f(R) gravity.
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Functional inequalities in quantum information theory
Functional inequalities constitute a very powerful toolkit in studying various problems arising in classical information theory, statistics and many-body systems. Extensions of these tools to the noncommutative setting have been introduced in the beginning of the 90's in order to study the …