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Relevant bibliographies by topics / Curvature of Ricci

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Academic literature on the topic 'Curvature of Ricci'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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Journal articles on the topic "Curvature of Ricci"

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Kloeckner, Benoît, and Stéphane Sabourau. "Mixed sectional-Ricci curvature obstructions on tori." Journal of Topology and Analysis 12, no. 03 (2018): 713–34. http://dx.doi.org/10.1142/s1793525319500626.

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We establish new obstruction results to the existence of Riemannian metrics on tori satisfying mixed bounds on both their sectional and Ricci curvatures. More precisely, from Lohkamp’s theorem, every torus of dimension at least three admits Riemannian metrics with negative Ricci curvature. We show that the sectional curvature of these metrics cannot be bounded from above by an arbitrarily small positive constant. In particular, if the Ricci curvature of a Riemannian torus is negative, bounded away from zero, then there exist some planar directions in this torus where the sectional curvature is

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Tripathi, Mukut Mani, та Jeong-Sik Kim. "C-totally real submanifolds in (κ,μ)-contact space forms". Bulletin of the Australian Mathematical Society 67, № 1 (2003): 51–65. http://dx.doi.org/10.1017/s0004972700033517.

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We obtain a basic B,-Y. Chen's inequality for a C-totally real submanifold in a (κ,μ)-contact space form involving intrinsic invariants, namely the scalar curvature and the sectional curvatures of the submanifold on left hand side and the main extrinsic invariant, namely the squared mean curvature on the right hand side. Inequalities between the squared mean curvature and Ricci curvature and between the squared mean curvature and κ-Ricci curvature are also obtained. These results are applied to get corresponding results for C-totally real submanifolds in a Sasakian space form.

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Aytpanova, Aray Amangeldiyevna. "RICCI CURVATURE AND THE RICCI OPERATOR." Theoretical & Applied Science 1, no. 05 (2013): 12–17. http://dx.doi.org/10.15863/tas.2013.05.1.3.

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Rovenski, Vladimir. "The weighted mixed curvature of a foliated manifold." Filomat 33, no. 4 (2019): 1097–105. http://dx.doi.org/10.2298/fil1904097r.

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We introduce the weighted mixed curvature of an almost product (e.g. foliated) Riemannian manifold equipped with a vector field. We define several qth Ricci type curvatures, which interpolate between the weighed sectional and Ricci curvatures. New concepts of the ?mixed-curvature-dimension condition? and ?synthetic dimension of a distribution? allow us to renew the estimate of the diameter of a compact Riemannian foliation and splitting results for almost product manifolds of nonnegative/nonpositive weighted mixed scalar curvature. We also study the Toponogov?s type conjecture on dimension of

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KNOPF, DAN. "POSITIVITY OF RICCI CURVATURE UNDER THE KÄHLER–RICCI FLOW." Communications in Contemporary Mathematics 08, no. 01 (2006): 123–33. http://dx.doi.org/10.1142/s0219199706002052.

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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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Li, Benling, and Zhongmin Shen. "Ricci Curvature Tensor and Non-Riemannian Quantities." Canadian Mathematical Bulletin 58, no. 3 (2015): 530–37. http://dx.doi.org/10.4153/cmb-2014-063-4.

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AbstractThere are several notions of Ricci curvature tensor in Finsler geometry and spray geometry. One of them is defined by the Hessian of the well-known Ricci curvature. In this paper we will introduce a new notion of Ricci curvature tensor and discuss its relationship with the Ricci curvature and some non-Riemannian quantities. Using this Ricci curvature tensor, we shall have a better understanding of these non-Riemannian quantities.

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Azarhooshang, Nazanin, Prithviraj Sengupta, and Bhaskar DasGupta. "A Review of and Some Results for Ollivier–Ricci Network Curvature." Mathematics 8, no. 9 (2020): 1416. http://dx.doi.org/10.3390/math8091416.

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Characterizing topological properties and anomalous behaviors of higher-dimensional topological spaces via notions of curvatures is by now quite common in mainstream physics and mathematics, and it is therefore natural to try to extend these notions from the non-network domains in a suitable way to the network science domain. In this article we discuss one such extension, namely Ollivier’s discretization of Ricci curvature. We first motivate, define and illustrate the Ollivier–Ricci Curvature. In the next section we provide some “not-previously-published” bounds on the exact and approximate co

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Tabatabaeifar, Tayebeh, Behzad Najafi, and Akbar Tayebi. "Weighted projective Ricci curvature in Finsler geometry." Mathematica Slovaca 71, no. 1 (2021): 183–98. http://dx.doi.org/10.1515/ms-2017-0446.

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Abstract In this paper, we introduce the weighted projective Ricci curvature as an extension of projective Ricci curvature introduced by Z. Shen. We characterize the class of Randers metrics of weighted projective Ricci flat curvature. We find the necessary and sufficient condition under which a Kropina metric has weighted projective Ricci flat curvature. Finally, we show that every projectively flat metric with isotropic weighted projective Ricci and isotropic S-curvature is a Kropina metric or Randers metric.

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Ma, Li. "Expanding Ricci solitons with pinched Ricci curvature." Kodai Mathematical Journal 34, no. 1 (2011): 140–43. http://dx.doi.org/10.2996/kmj/1301576768.

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SHEN, ZHONGMIN, and GUOJUN YANG. "RANDERS METRICS OF REVERSIBLE CURVATURE." International Journal of Mathematics 24, no. 01 (2013): 1350006. http://dx.doi.org/10.1142/s0129167x13500067.

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In this paper, we introduce the notions of R-reversibility and Ricci-reversibility. We prove that Randers metrics are R-reversible or Ricci-reversible if and only if they are R-quadratic or Ricci-quadratic, respectively. Besides, we discuss the properties of Ricci- or R-reversible Randers metrics which are also weakly Einsteinian, or Douglassian, or of scalar flag curvature. In particular, we determine the local structure of Randers metrics which are Ricci-reversible and locally projectively flat, and prove that an n (≥ 3)-dimensional Ricci-reversible Randers metric of non-zero scalar flag cur

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Dissertations / Theses on the topic "Curvature of Ricci"

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Hinde, Colin Douglas. "The essence of Ricci curvature." Diss., Restricted to subscribing institutions, 2008. http://proquest.umi.com/pqdweb?did=1619436071&sid=1&Fmt=2&clientId=1564&RQT=309&VName=PQD.

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Honda, Shouhei. "Ricci curvature and almost spherical multi-suspension." 京都大学 (Kyoto University), 2009. http://hdl.handle.net/2433/126578.

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Kyoto University (京都大学)<br>0048<br>新制・課程博士<br>博士(理学)<br>甲第14991号<br>理博第3470号<br>新制||理||1508(附属図書館)<br>27441<br>UT51-2009-R715<br>京都大学大学院理学研究科数学・数理解析専攻<br>(主査)教授深谷賢治, 教授河野明, 教授加藤毅<br>学位規則第4条第1項該当

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Rose, Christian. "Heat kernel estimates based on Ricci curvature integral bounds." Doctoral thesis, Universitätsbibliothek Chemnitz, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-228681.

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Any Riemannian manifold possesses a minimal solution of the heat equation for the Dirichlet Laplacian, called the heat kernel. During the last decades many authors investigated geometric properties of the manifold such that its heat kernel fulfills a so-called Gaussian upper bound. Especially compact and non-compact manifolds with lower bounded Ricci curvature have been examined and provide such Gaussian estimates. In the compact case it ended even with integral Ricci curvature assumptions. The important techniques to obtain Gaussian bounds are the symmetrization procedure for compact manifold

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Lohkamp, Joachim. "Existenz von Metriken negativer Ricci-Krümmung." Bonn : [s.n.], 1992. http://catalog.hathitrust.org/api/volumes/oclc/29040814.html.

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Fritz, Hans [Verfasser], and Gerhard [Akademischer Betreuer] Dziuk. "Finite element approximation of Ricci Curvature and simulation of Ricci-DeTurck Flow = Finite Elemente Approximation der Ricci-Krümmung und Simulation des Ricci-DeTurck-Flusses." Freiburg : Universität, 2013. http://d-nb.info/1123476411/34.

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Targino, Renato Oliveira. "A Curvatura de Gauss-Kronecker de hipersuperfÃcies mÃnimas em formas espaciais 4-dimensionais." Universidade Federal do CearÃ, 2011. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=6672.

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CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior<br>Neste trabalho estudamos hipersuperfÃcies mÃnimas completas e com curvatura de Gauss-Kronecker constante em uma forma espacial Q4(c). Provamos que o Ãnfimo do valor absoluto da curvatura de Gauss-Kronecker de uma hipersuperfÃcie mÃnima completa em Q4(c); c ≤ 0; na qual a curvatura de Ricci Ã limitado inferiormente, Ã igual a zero. AlÃm disso, estudamos hipersuperfÃcies mÃnimas conexas M3 em uma forma espacial Q4(c) com curvatura de Gauss-Kronecker K constante. Para o caso c ≤ 0, provamos, por um argumento local, que se

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Pimentel, Soraya Bianca Souza, and 92-98450-7876. "H-Quase Sóliton de Ricci." Universidade Federal do Amazonas, 2016. https://tede.ufam.edu.br/handle/tede/6392.

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Submitted by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2018-05-22T14:42:33Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) h-Quase Sóliton de Ricci.pdf: 40561599 bytes, checksum: 88a9a69eec01fab6046ed43b9b7d63b9 (MD5)<br>Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2018-05-22T14:42:51Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) h-Quase Sóliton de Ricci.pdf: 40561599 bytes, checksum: 88a9a69eec01fab6046ed43b9

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Kell, Martin. "On curvature conditions using Wasserstein spaces." Doctoral thesis, Universitätsbibliothek Leipzig, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-149614.

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This thesis is twofold. In the first part, a proof of the interpolation inequality along geodesics in p-Wasserstein spaces is given and a new curvature condition on abstract metric measure spaces is defined. In the second part of the thesis a proof of the identification of the q-heat equation with the gradient flow of the Renyi (3-p)-Renyi entropy functional in the p-Wasserstein space is given. For that, a further study of the q-heat flow is presented including a condition for its mass preservation.

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Lima, Marcos César de Vasconcelos. "Variedades completas com espectro positivo." reponame:Repositório Institucional da UFC, 2011. http://www.repositorio.ufc.br/handle/riufc/25067.

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LIMA, Marcos Cesar Vasconcelos. Variedades completas com espectro positivo. 2011. 53 f. Dissertação (Mestrado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2011.<br>Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-08-24T16:54:57Z No. of bitstreams: 1 2011_dis_mcvlima.pdf: 397902 bytes, checksum: 57fa923d41f8ebc402900120bee15521 (MD5)<br>Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2017-08-25T11:09:14Z (GMT) No. of bitstreams: 1 2011_dis_mcvlima.pdf: 397902 bytes, checksum: 57fa923d41f8ebc402900120bee15521 (MD5)<br>Made available in

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Ketterer, Christian Eugen Michael [Verfasser]. "Ricci curvature bounds for warped products and cones / Christian Eugen Michael Ketterer." Bonn : Universitäts- und Landesbibliothek Bonn, 2014. http://d-nb.info/1238687571/34.

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Books on the topic "Curvature of Ricci"

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author, Tian Gang 1958, ed. The geometrization conjecture. American Mathematical Society, 2014.

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The Poincaré conjecture: Clay Research Conference, resolution of the Poincaré conjecture, Institute Henri Poincaré, Paris, France, June 8-9, 2010. American Mathematical Society, 2014.

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Wentworth, Richard A., Duong H. Phong, Paul M. N. Feehan, Jian Song, and Ben Weinkove. Analysis, complex geometry, and mathematical physics: In honor of Duong H. Phong : May 7-11, 2013, Columbia University, New York, New York. American Mathematical Society, 2015.

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Book chapters on the topic "Curvature of Ricci"

1

Villani, Cédric. "Ricci curvature." In Grundlehren der mathematischen Wissenschaften. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-71050-9_14.

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Petersen, Peter. "Ricci Curvature Comparison." In Graduate Texts in Mathematics. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-26654-1_7.

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Aubin, Thierry. "The Ricci Curvature." In Some Nonlinear Problems in Riemannian Geometry. Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-13006-3_9.

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Petersen, Peter. "Ricci Curvature Comparison." In Graduate Texts in Mathematics. Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4757-6434-5_9.

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Cheng, Xinyue, and Zhongmin Shen. "Riemann Curvature and Ricci Curvature." In Finsler Geometry. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-24888-7_4.

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Chow, Bennett, Peng Lu, and Lei Ni. "Closed 3-manifolds with positive Ricci curvature." In Hamilton’s Ricci Flow. American Mathematical Society, 2006. http://dx.doi.org/10.1090/gsm/077/03.

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Maas, Jan. "Entropic Ricci Curvature for Discrete Spaces." In Modern Approaches to Discrete Curvature. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-58002-9_5.

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Chow, Bennett, and Dan Knopf. "Three-manifolds of positive Ricci curvature." In Mathematical Surveys and Monographs. American Mathematical Society, 2004. http://dx.doi.org/10.1090/surv/110/06.

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Ni, Lei. "Ricci flow and manifolds with positive curvature." In Symmetry: Representation Theory and Its Applications. Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-1590-3_17.

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Gallot, Sylvestre, Dominique Hulin, and Jacques Lafontaine. "Analysis on Manifolds and the Ricci Curvature." In Universitext. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-97026-9_4.

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Conference papers on the topic "Curvature of Ricci"

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Tao, Mo, Shaoping Wang, Hong Chen, Zhi Liu, and Yi Lei. "Information Manifold and Ricci Curvature." In 2021 IEEE International Conference on Mechatronics and Automation (ICMA). IEEE, 2021. http://dx.doi.org/10.1109/icma52036.2021.9512823.

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Ni, Chien-Chun, Yu-Yao Lin, Jie Gao, Xianfeng David Gu, and Emil Saucan. "Ricci curvature of the Internet topology." In IEEE INFOCOM 2015 - IEEE Conference on Computer Communications. IEEE, 2015. http://dx.doi.org/10.1109/infocom.2015.7218668.

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Xu, Eilza, Richard C. Wilson, and Edwin R. Hancock. "Curvature Estimation for Ricci Flow Embedding." In 2014 22nd International Conference on Pattern Recognition (ICPR). IEEE, 2014. http://dx.doi.org/10.1109/icpr.2014.277.

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Saucan, Emil, Gershon Wolansky, Eli Appleboim, and Yehoshua Y. Zeevi. "Combinatorial Ricci Curvature and Laplacians for Image Processing." In 2009 2nd International Congress on Image and Signal Processing (CISP). IEEE, 2009. http://dx.doi.org/10.1109/cisp.2009.5304710.

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Guo, Xuan, Qiang Tian, Wang Zhang, Wenjun Wang, and Pengfei Jiao. "Learning Stochastic Equivalence based on Discrete Ricci Curvature." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/201.

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Role-based network embedding methods aim to preserve node-centric connectivity patterns, which are expressions of node roles, into low-dimensional vectors. However, almost all the existing methods are designed for capturing a relaxation of automorphic equivalence or regular equivalence. They may be good at structure identification but could show poorer performance on role identification. Because automorphic equivalence and regular equivalence strictly tie the role of a node to the identities of all its neighbors. To mitigate this problem, we construct a framework called Curvature-based Network

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Lin, A. Shu, B. Zhongxuan Luo, C. Jielin Zhang, and D. Emil Saucan. "Generalized Ricci curvature based sampling and reconstruction of images." In 2015 23rd European Signal Processing Conference (EUSIPCO). IEEE, 2015. http://dx.doi.org/10.1109/eusipco.2015.7362454.

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Marques, Fernando Codá. "Scalar Curvature, Conformal Geometry, and the Ricci Flow with Surgery." In Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). Published by Hindustan Book Agency (HBA), India. WSPC Distribute for All Markets Except in India, 2011. http://dx.doi.org/10.1142/9789814324359_0075.

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Jonckheere, Edmond, and Eugenio Grippo. "Ollivier-Ricci Curvature Approach to Cost-Effective Power Grid Congestion Management." In 2019 Chinese Control And Decision Conference (CCDC). IEEE, 2019. http://dx.doi.org/10.1109/ccdc.2019.8832819.

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Whidden, Chris, and Frederick A. Matsen. "Ricci-Ollivier Curvature of the Rooted Phylogenetic Subtree-Prune-Regraft Graph." In 2016 Proceedings of the Thirteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO). Society for Industrial and Applied Mathematics, 2015. http://dx.doi.org/10.1137/1.9781611974324.6.

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Gilkey, P., S. Nikčević, and D. Westerman. "RIEMANNIAN GEOMETRIC REALIZATIONS FOR RICCI TENSORS OF GENERALIZED ALGEBRAIC CURVATURE OPERATORS." In Proceedings of the VIII International Colloquium. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814261173_0017.

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