Niky Kamran N. April 3, 1 Introduction. To the best of our knowledge, the study of the local symplectic invariants of submanifolds of Euclidean space was initiated by Chern and Wang in , . They considered mainly the case of curves and hypersurfaces, and obtained structure equations defining a set of local symplectic differential invariants for these objects. This is in contrast with the case in which one considers the full infinite-dimensional symplectomorphism group of the ambient R2n. Indeed, in the latter case, the theorem of Darboux implies that submanifolds have no local differential invariants.
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History Of Mathematics Back cover copy This volume of selected academic papers demonstrates the significance of the contribution to mathematics made by Manfredo P.
Twice a Guggenheim Fellow and the winner of many prestigious national and international awards, the professor at the institute of Pure and Applied Mathematics in Rio de Janeiro is well known as the author of influential textbooks such as Differential Geometry of Curves and Surfaces.
Aspects covered in the featured papers include relations between curvature and topology, convexity and rigidity, minimal surfaces, and conformal immersions, among others. Offering more than just a retrospective focus, the volume deals with subjects of current interest to researchers, including a paper co-authored with Frank Warner on the convexity of hypersurfaces in space forms.
It also presents the basic stability results for minimal surfaces in the Euclidean space obtained by the author and his collaborators. Students of Manfredo P. His work, as presented in this collection of 32 papers, speaks for itself, as regards both its breadth and its depth, and this volume is an appropriate tribute to him. It is of the highest quality.
This list extends to more than 80 research articles and several books that set milestones in differential geometry. The increase of research on differential geometry in Brazil is thus rigorously documented and the result presented as fundamental reading for this field.
Manfredo do Carmo
Membro do Com. Soliton solutions to the curve shortening flow on the sphere. The mean curvature flow by parallel hypersurfaces. Geometry Seminar, Istanbul University. On Backlund and Ribaucour transformations for surfaces with constant negative curvature.
Keti Tenenblat Introdução à geometria diferencial Edgard Blucher (2008).pdf