Busemann functions on ℜ_RI m n and ℜ_IV n

Abstract

The Busemann function plays a very important role in studying topology and geometry of a complete Riemannian manifold. In this paper the Busemann functions on the real classical domain of the first type and the Cartan domain of the fourth type in the explicit formulas are obtained.

Keywords:

• Busemann function
• geodesic ray
• Cartan domain of the fourth type

Supported by the National Natural Science Foundation of China (Grant No. 10071051) and Natural Science Foundation of Beijing (Grant No. 1002004)

Supported by the National Natural Science Foundation of China (Grant No. 10071051) and Natural Science Foundation of Beijing (Grant No. 1002004)

Notes

Supported by the National Natural Science Foundation of China (Grant No. 10071051) and Natural Science Foundation of Beijing (Grant No. 1002004)