Geometry of Differential Space
نویسندگان
چکیده
منابع مشابه
Differential Geometry of Submanifolds of Projective Space
These are lecture notes on the rigidity of submanifolds of projective space “resembling” compact Hermitian symmetric spaces in their homogeneous embeddings. The results of [16, 20, 29, 18, 19, 10, 31] are surveyed, along with their classical predecessors. The notes include an introduction to moving frames in projective geometry, an exposition of the Hwang-Yamaguchi ridgidity theorem and a new v...
متن کاملDifferential Geometry on Compound Poisson Space
In this paper we carry out analysis and geometry for a class of infinite dimensional manifolds, namely, compound configuration spaces as a natural generalization of the work [AKR98a]. More precisely a differential geometry is constructed on the compound configuration space ΩX over a Riemannian manifold X. This geometry is obtained as a natural lifting of the Riemannian structure on X. In partic...
متن کاملDifferential Geometry of Submanifolds of Projective Space: Rough Draft
• Introduction to the local differential geometry of submanifolds of projective space • Introduction to moving frames for projective geometry • How much must a submanifold X ⊂ PN resemble a given submanifold Z ⊂ PM infinitesimally before we can conclude X ≃ Z? • To what order must a line field on a submanifold X ⊂ PN have contact with X before we can conclude the lines are contained in X? • App...
متن کاملOn the differential geometry of curves in Minkowski space
We discuss some aspects of the differential geometry of curves in Minkowski space. We establish the Serret-Frenet equations in Minkowski space and use them to give a very simple proof of the fundamental theorem of curves in Minkowski space. We also state and prove two other theorems which represent Minkowskian versions of a very known theorem of the differential geometry of curves in tridimensi...
متن کاملDIFFERENTIAL GEOMETRY OF CURVES AND SURFACES 2. Curves in Space
for a < t < b. The entire Section 1.3 of the notes can be immediately reformulated for curves in the space: Definition 1.3.2 (of the length of a curve over a closed interval), Definition 1.3.3 and Theorem 1.3.4 (concerning reparametrization of curves), Definition 1.3.4 (of a regular curve), Theorem 1.3.6 and Proposition 1.3.7 (concerning parametrization by arc length). As about Section 1.4 (tha...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1973
ISSN: 0091-1798
DOI: 10.1214/aop/1176996973