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Identifier 000423971
Title Curvature in sub-riemannian geometry
Alternative Title Καμπυλότητα στην υπό-ριμάνεια γεωμετρία
Author Φουρτζής, Ιωάννης
Thesis advisor Πλατής, Ιωάννης
Abstract In Chapter 2 we present the main de_nitions that will be used throughout the text. In Chapter 3 we de_ne the connections that will be used throughout the text. In Chapter 4 we discuss the notions of Sub-Riemannian curvature and sectional curvature as well as Bianchi Identities. In Chapter 5 we de- _ne the Sub-Riemannian Ricci curvature and the notion of horizontal scalar curvature, prove the Contracted Bianchi Identity, de_ne the gradient of a tensor, the Hessian, the horizontal Laplacian and vertical rigidity. Finally, in Chapter 6, we discuss the di_erences between the Sub-Riemannian connection and the Levi-Civita connection and state a Sub-Riemannian version of the Bonnet-Myers theorem
Language English
Subject Mαnifold
Issue date 2019-07-26
Collection   School/Department--School of Sciences and Engineering--Department of Mathematics and Applied Mathematics--Post-graduate theses
  Type of Work--Post-graduate theses
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