Communications of the
Korean Mathematical Society CKMS

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Commun. Korean Math. Soc. 2010; 25(1): 83-96

Printed March 1, 2010

https://doi.org/10.4134/CKMS.2010.25.1.83

Copyright © The Korean Mathematical Society.

Geodesic spheres and balls of the Heisenberg groups

Changrim Jang, Jihye Park, and Keun Park

University of Ulsan, Myung-Duk Girl's Middle School, and University of Ulsan

Abstract

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Let $\mathbb H^{2n+1}$ be the $(2n+1)$-dimensional Heisenberg group equipped with a left-invariant metric. In this paper we study the Gaussian curvatures of the geodesic spheres and the volumes of geodesic balls in $\mathbb H^{2n+1}.$

Keywords: Heisenberg group, geodesic sphere, geodesic ball

MSC numbers: 53C22, 22E25

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