Καμπυλότητα στην υπό-ριμάνεια γεωμετρία

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 theore