On the Ricci curvature of 3-submanifolds in the unit sphere
Sign Up to like & getrecommendations! Published in 2020 at "Archiv der Mathematik"
DOI: 10.1007/s00013-020-01515-7
Abstract: In this short note, studying 3-dimensional compact and minimal submanifolds of the $$(3+p)$$ ( 3 + p ) -dimensional unit sphere $${\mathbb {S}}^{3+p}(1)$$ S 3 + p ( 1 ) , we establish two rigidity… read more here.
Keywords: unit sphere; curvature submanifolds; submanifolds unit; ricci curvature ... See more keywords
Negative Ricci curvature on some non-solvable Lie groups II
Sign Up to like & getrecommendations! Published in 2019 at "Mathematische Zeitschrift"
DOI: 10.1007/s00209-019-02310-z
Abstract: We construct many examples of Lie groups admitting a left-invariant metric of negative Ricci curvature. We study Lie algebras which are semidirect products $${\mathfrak {l}}= ({\mathfrak {a}} \oplus {\mathfrak {u}} ) < imes {\mathfrak {n}}$$… read more here.
Keywords: mathfrak; ricci curvature; lie groups; mathfrak mathfrak ... See more keywords
Negative Ricci curvature on some non-solvable Lie groups
Sign Up to like & getrecommendations! Published in 2017 at "Geometriae Dedicata"
DOI: 10.1007/s10711-016-0185-x
Abstract: We show that for any non-trivial representation $$(V, \pi )$$(V,π) of $$\mathfrak {u}(2)$$u(2) with the center acting as multiples of the identity, the semidirect product $$\mathfrak {u}(2) \ltimes _\pi V$$u(2)⋉πV admits a metric with negative… read more here.
Keywords: metric negative; negative ricci; solvable lie; ricci curvature ... See more keywords
Boundary effect of m-dimensional Bakry-Émery Ricci curvature
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DOI: 10.1007/s13324-018-0237-5
Abstract: We consider how m-dimensional Bakry-Émery Ricci curvature affects the geometry of the boundary $$\partial M$$∂M. By using the Reilly’s formula with respect to f-Laplacian, geometric inequalities involving f-mean curvature are obtained. Furthermore, we also achieve… read more here.
Keywords: mery ricci; ricci curvature; bakry mery; dimensional bakry ... See more keywords
Ricci curvature and the manifold learning problem
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DOI: 10.1016/j.aim.2018.11.001
Abstract: Consider a sample of $n$ points taken i.i.d from a submanifold $\Sigma$ of Euclidean space. We show that there is a way to estimate the Ricci curvature of $\Sigma$ with respect to the induced metric… read more here.
Keywords: ricci curvature; learning problem; curvature manifold; manifold learning ... See more keywords
On a class of projectively Ricci-flat Finsler metrics
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DOI: 10.1016/j.difgeo.2020.101680
Abstract: Abstract Every Finsler metric induces a spray on a manifold. With a volume form on a manifold, every spray can be deformed to a projective spray. The Ricci curvature of a projective spray is called… read more here.
Keywords: finsler metrics; ricci flat; finsler; ricci curvature ... See more keywords
Harnack inequality, heat kernel bounds and eigenvalue estimates under integral Ricci curvature bounds
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DOI: 10.1016/j.jde.2020.01.003
Abstract: Abstract Let ( M n , g i j ) be a complete Riemannian manifold. We prove that for any p > n 2 , when k ( p , 1 ) is small enough,… read more here.
Keywords: curvature bounds; integral ricci; ricci curvature; heat ... See more keywords
Segment Inequality and Almost Rigidity Structures for Integral Ricci Curvature
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DOI: 10.1093/imrn/rnab065
Abstract: We will show the Cheeger–Colding segment inequality for manifolds with integral Ricci curvature bound. By using this segment inequality, the almost rigidity structure results for integral Ricci curvature will be derived by a similar method… read more here.
Keywords: integral ricci; ricci curvature; segment inequality;
Introducing quantum Ricci curvature
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DOI: 10.1103/physrevd.97.046008
Abstract: Motivated by the search for geometric observables in nonperturbative quantum gravity, we define a notion of coarse-grained Ricci curvature. It is based on a particular way of extracting the local Ricci curvature of a smooth… read more here.
Keywords: introducing quantum; quantum ricci; curvature; ricci curvature ... See more keywords
Positive Ricci curvature on fiber bundles with compact structure group
Sign Up to like & getrecommendations! Published in 2022 at "Advances in Geometry"
DOI: 10.1515/advgeom-2021-0007
Abstract: Abstract This paper presents a direct and simple proof of a result concerning the existence of metrics of positive Ricci curvature on the total space of fiber bundles with compact structure groups. In particular, it… read more here.
Keywords: compact structure; bundles compact; fiber bundles; positive ricci ... See more keywords
Long-Scale Ollivier Ricci Curvature of Graphs
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DOI: 10.1515/agms-2019-0003
Abstract: Abstract We study the long-scale Ollivier Ricci curvature of graphs as a function of the chosen idleness. Similarly to the previous work on the short-scale case, we show that this idleness function is concave and… read more here.
Keywords: long scale; graphs; ollivier ricci; ricci curvature ... See more keywords