Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2010; 25(3): 451-456

Printed September 1, 2010

https://doi.org/10.4134/CKMS.2010.25.3.451

Copyright © The Korean Mathematical Society.

Explicit examples of K\{a}hler metrics on the ellipsoids

Kwang-Soon Park

Seoul National University

Abstract

In this paper, we construct explicitly K\"{a}hler metrics on the ellipsoids and calculate their sectional curvatures. Using MAPLE [3], we obtain some geodesic curves on an ellipsoid so that if some conditions are dropped in Question 2.1 [4], then Question 2.1 is not true.

Keywords: K\"{a}hler metric, sectional curvature, minimal geodesic curve

MSC numbers: 53C55, 53C22