Showing papers in "Duke Mathematical Journal in 1978"

Complex differential and integral geometry and curvature integrals associated to singularities of complex analytic varieties

Abstract: Introduction 1. Hermann Weyl's formula for the volume of tubes and the Gauss-Bonnet theorem a) Frames and derivation of the formula 432 b) Tubes and the Gauss-Bonnet theorem 437 c) Gauss mapping and the Gauss-Bonnet theorem 440 Footnotes 443 2. Integral geometry for manifolds in IR N a) Crofton's formula in the plane 444 b) Application of Crofton's formula to total curvature 447 c) The kinematic formula 451 Footnotes 454 3. Hermitian differential geometry and volumes of tubes in the complex case a) Frames and Chern forms for complex manifolds in N 454 b) Remarks on integration over analytic varieties 463 c) Volume of tubes in the complex case 467 Footnotes 472 4. Hermitian integral geometry a) The elementary version of Crofton's formula 472 b) Crofton's formula for Schubert cycles 476 c) The second Crofton formula 479 d) The third Crofton formula 485 Appendix to Sections 2 and 4: Some general observations on integral geometry 492 Footnotes 496 5. Curvature and Pliicker defects a) Gauss-Bonnet and the Plficker paradox 496 b) The Pliicker defect and Langevin's formula 500 c) Extension to higher codimension and isolation of the top Milnor number 505 d) Further generalizations and open questions 506 Footnotes 512