Finsler geometry generalizes Riemannian geometry in the same sense that Banach spaces generalize Hilbert spaces. This book presents an expository account of seven important topics in Riemann-Finsler geometry, ones which have recently undergone significant development but have not had a detailed pedagogical treatment elsewhere. Each article will open the door to an active area of research, and is suitable for a special topics course in graduate-level differential geometry. The contributors consider issues related to volume, geodesics, curvature, complex differential geometry, and parametrized...
Finsler geometry generalizes Riemannian geometry in the same sense that Banach spaces generalize Hilbert spaces. This book presents an expository acco...
This book investigates the geometry of complex subvarieties of compact Hermitian symmetric spaces, particularly the complex Grassmannians, which are central to Schubert calculus and its applications to enumerative algebraic geometry. To do so, Robert Bryant employs a combination of Hermitian differential geometry, calibrations, and classical moving frame constructions.
The main result is that, for Hermitian symmetric spaces M of rank greater than 1, there are homology classes c (called extremal) such that the complex varieties V in M that represent c display rigidity in...
This book investigates the geometry of complex subvarieties of compact Hermitian symmetric spaces, particularly the complex Grassmannians, whic...
This book gives a treatment of exterior differential systems. It will in clude both the general theory and various applications. An exterior differential system is a system of equations on a manifold defined by equating to zero a number of exterior differential forms. When all the forms are linear, it is called a pfaffian system. Our object is to study its integral manifolds, i. e., submanifolds satisfying all the equations of the system. A fundamental fact is that every equation implies the one obtained by exterior differentiation, so that the complete set of equations associated to an...
This book gives a treatment of exterior differential systems. It will in clude both the general theory and various applications. An exterior different...