# On Riemannian geometry of tangent sphere bundles with arbitrary constant radius

## Oldřich Kowalski and Masami Sekizawa

Address:

Faculty of Mathematics and Physics Charles University in Prague Sokolovská 83, 186 75 Praha 8, Czech Republic

Department of Mathematics Tokyo Gakugei University Koganei-shi Nukuikita-machi 4-1-1, Tokyo 184-8501, Japan

E-mail:

kowalski@karlin.mff.cuni.cz

sekizawa@u-gakugei.ac.jp

Abstract: We shall survey our work on Riemannian geometry of tangent sphere bundles with arbitrary constant radius done since the year 2000.

AMSclassification: primary 53C07; secondary 53C30, 53C25.

Keywords: Riemannian metric, tangent bundle, tangent sphere bundle, Riemannian curvature, scalar curvature.