Conjugation of the classical kernels of Bochner-Martinelli & Koppelman-Leray with the FBI transform is used to construct homotopy operators in the tangential Cauchy-Riemann complex. On a real hypersurface in complex space and the presence of supporting manifolds is exploited to …
Presents the basics of Riemannian geometry in its modern form as geometry of differentiable manifolds and the important structures on them. This book shows that Riemannian geometry has a great influence to several fundamental areas of modern mathematics and its applications.
Clifford algebras are assuming now an increasing role in theoretical physics. Some of them predominantly larger ones are used in elementary particle theory, especially for a unification of the fundamental interactions. The smaller ones are promoted in more classical domains. Thi…
Visual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton's geometrical methods to provide geometrical explanations of the …
"Visual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton's geometrical methods to provide geometrical explanations of the…
In this work, I have attempted to give a coherent exposition of the theory of differential forms on a manifold and harmonic forms on a Riemannian space. The concept of a current, a notion so general that it includes as special cases both differential forms and chains, is the key…