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Advances in Geometry

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Skew symmetric logarithms and geodesics on On(ℝ)

Alberto Dolcetti
  • Corresponding author
  • Dipartimento di Matematica e Informatica “Ulisse Dini”, Viale Morgagni 67/a, 50134 Firenze, Italia
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/ Donato Pertici
Published Online: 2018-07-20 | DOI: https://doi.org/10.1515/advgeom-2018-0012

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.

Keywords: Skew symmetric and orthogonal matrices; Singular Value Decomposition of skew symmetric matrices; Pfaffian; exponential map; skew symmetric and principal logarithms; trace and Frobenius metrics; Riemannian manifolds; geodesic curves; diameter; pairs of (weakly) diametral orthogonal matrices

MSC 2010: 15A16; 53C22

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About the article


Received: 2015-07-13

Revised: 2016-08-22

Published Online: 2018-07-20


Funding: This research was partially supported by MIUR-PRIN: “Varietà reali e complesse: geometria, topologia e analisi armonica” and by GNSAGA-INdAM.


Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2018-0012.

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