Submersions on nilmanifolds and their geodesics
Copyright policy )Submersions on nilmanifolds and their geodesics
Summary: We describe the geodesics of two-step nilpotent Lie groups \(N\) with respect to left invariant Riemannian metrics \(\langle. ,.\rangle\) using the Riemannian submersion structure of the fiber bundle \(\pi :N\rightarrow N/\mathcal Z\), where \(\mathcal Z\) denotes the center of \(N\). We characterize two-step nilmanifolds \((N,\langle. ,.\rangle)\) which have the property that the projections of geodesics of \(N\) onto the factor space \(N/\mathcal Z\) are Euclidean lines or circles.
Differential geometry of homogeneous manifolds, Nilpotent and solvable Lie groups, Riemannian submersion, two-step nilpotent Lie groups, nilmanifolds, H-type groups, Global Riemannian geometry, including pinching
Differential geometry of homogeneous manifolds, Nilpotent and solvable Lie groups, Riemannian submersion, two-step nilpotent Lie groups, nilmanifolds, H-type groups, Global Riemannian geometry, including pinching
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