| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
|
|---|
| Research Abstract |
We investigated Riemannian geometry and Fisher information geometry of the Poisson kernel map φ from an Hadamard manifold X into the space P(∂X) of probability measures of positive density function, absolutely continous with respect to the Riemannian volume, defined on the ideal boundary of X. We obtained the following results : if the mapφ is homothetic and minimal, then the Poisson kernel is represented in terms of the Busemann function so that X turns out to be asymptotically harmonic and satisfies the axiom of visibility and furthermore we can show that this homothetic constant coincides with the volume entropy of X.
|
