Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series A, Pt. 3, pp. 419--424

SOME QUESTIONS ON INTEGRAL GEOMETRY ON RIEMANNIAN MANIFOLDS

By

VISHWAMBHAR PATI and ALLADI SITARAM, Indian Statistical Institute, Bangalore

SUMMARY. It is a surprising but known fact that an L1 function on Rn is determined once all its spherical averages with centres coming from certain ``small'' sets are known. We generalise this result to complete connected real-analytic Riemannian manifolds with a real-analytic metric (with some curvature restrictions), where superisothermal sets play the same role as balls do in the case of Euclidean space.

AMS (1991) subject classification. 53C65.

Key words and phrases. Integral geometry, heat kernel, Riemannian manifold.

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