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Aspects of flat Radon transforms. (English) Zbl 0785.44002
Grinberg, Eric L. (ed.), Geometric analysis. Proceedings of an AMS special session, held at the 868th meeting of the American Mathematical Society at Temple University, Philadelphia, PA, USA, October 12-13, 1991. Providence, RI: American Mathematical Society. Contemp. Math. 140, 73-85 (1992).
Summary: Starting with \(X\) a compact symmetric space we consider the operator of integration along maximal totally geodesic flat submanifolds. By working out some explicit examples we show that either this transform is injective or else there is an obvious kernel arising from symmetry considerations and, passing to a quotient, we obtain injectivity.
For the entire collection see [Zbl 0773.00025].

44A12 Radon transform
43A85 Harmonic analysis on homogeneous spaces
53C55 Global differential geometry of Hermitian and Kählerian manifolds