Skew symmetric logarithms and geodesics on On(ℝ)
-
Alberto Dolcetti
and
Donato Pertici
Abstract
We investigate the connections between the differential-geometric properties of the exponential map from the space of real skew symmetric matrices onto the group of real special orthogonal matrices and the manifold of real orthogonal matrices equipped with the Riemannian structure induced by the Frobenius metric.
Acknowledgements
We want to thank the anonymous referee for many useful and precious suggestions about the matter and the writing of this paper.
Funding: This research was partially supported by MIUR-PRIN: “Varietà reali e complesse: geometria, topologia e analisi armonica” and by GNSAGA-INdAM.
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Articles in the same Issue
- Frontmatter
- The index of symmetry of three-dimensional Lie groups with a left-invariant metric
- Canonical contact unit cotangent bundle
- On the umbilicity of generalized linear Weingarten hypersurfaces in hyperbolic spaces
- Regular polyhedra in the 3-torus
- Rational curves on Del Pezzo manifolds
- Commuting matrices and the Hilbert scheme of points on affine spaces
- On rational varieties of small rationality degree
- Skew symmetric logarithms and geodesics on On(ℝ)
- New homogeneous Einstein metrics on quaternionic Stiefel manifolds
Articles in the same Issue
- Frontmatter
- The index of symmetry of three-dimensional Lie groups with a left-invariant metric
- Canonical contact unit cotangent bundle
- On the umbilicity of generalized linear Weingarten hypersurfaces in hyperbolic spaces
- Regular polyhedra in the 3-torus
- Rational curves on Del Pezzo manifolds
- Commuting matrices and the Hilbert scheme of points on affine spaces
- On rational varieties of small rationality degree
- Skew symmetric logarithms and geodesics on On(ℝ)
- New homogeneous Einstein metrics on quaternionic Stiefel manifolds
