Surfaces of revolution admitting strongly convex slope metrics

Authors

  • P. Chansangiam King Mongkuts Institute of Technology Ladkrabang, Thailand
  • P. Chansri King Mongkuts Institute of Technology Ladkrabang, Thailand
  • S.V. Sabau Tokai University, Japan

DOI:

https://doi.org/10.31926/but.mif.2020.13.62.1.7

Keywords:

slope metric, surface of revolution, strong convexity

Abstract

This paper discusses the geometry of a surface endowed with a slope metric. We obtain necessary and sufficient conditions for any surface of revolution to admit a strongly convex slope metric. Such conditions involve certain inequalities for the derivative of the associated function on the Cartesian coordinate and the polar coordinate. In particular, we apply this result to a certain well-known surface of revolution.

Author Biographies

P. Chansangiam, King Mongkuts Institute of Technology Ladkrabang, Thailand

Department of Mathematics, Faculty of Science

P. Chansri, King Mongkuts Institute of Technology Ladkrabang, Thailand

Department of Mathematics, Faculty of Science

S.V. Sabau, Tokai University, Japan

Department of Biology, 5-1-1-1 Minamisawa, Minamiku, Sapporo 005-8601

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Published

2020-07-22

Issue

Vol. 13(62) No. 1 (2020)

Section

MATHEMATICS