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In this note we prove a conjecture of Kashiwara, which states that the Euler class of a coherent analytic sheaf F on a complex manifold X is the product of the Chern character of F with the Todd class of X. As a corollary, we obtain a functorial proof of the Grothendieck–Riemann–Roch theorem in Hodge cohomology for complex manifolds.

We consider complex projective space with its Fubini–Study metric and the X-ray transform defined by integration over its geodesics. We identify the kernel of this transform acting on symmetric tensor fields.

No abstract uploaded!

No abstract uploaded!