By Bang-yen Chen

Show description

Read Online or Download Geometry of submanifolds and its applications PDF

Similar differential geometry books

Download e-book for kindle: The topology of fibre bundles by Norman Steenrod

Fibre bundles, now an essential component of differential geometry, also are of significant value in sleek physics - akin to in gauge thought. This e-book, a succinct creation to the topic through renown mathematician Norman Steenrod, was once the 1st to offer the topic systematically. It starts with a common advent to bundles, together with such themes as differentiable manifolds and masking areas.

Download PDF by I. Chavel, H.M. Farkas: Differential geometry and complex analysis: a volume

Chavel I. , Farkas H. M. (eds. ) Differential geometry and intricate research (Springer, 1985)(ISBN 354013543X)(236s)

Download e-book for kindle: Theorems on regularity and singularity of energy minimizing by Leon Simon

The purpose of those lecture notes is to provide an primarily self-contained advent to the fundamental regularity idea for power minimizing maps, together with contemporary advancements in regards to the constitution of the singular set and asymptotics on method of the singular set. really good wisdom in partial differential equations or the geometric calculus of diversifications is no longer required.

Extra resources for Geometry of submanifolds and its applications

Sample text

DUP) Z = 0. Bejancu informed me that he also obtained this proposition independently. In Bejancu, Kon and Yano (1980), they proved that if 17P= 0 and N is anti- By an anti-holomorphic submanifold, we holomorphic, then N is a CR-product. mean a CR-submanifold with Jy-( = T 1N. 2. 3) r< 4h2 + 4h + p2 - p The equality holds if and only if (a) N Zies in a totaZZy geodesic C Ph+p+hp of CFJ, (b) ZocaZZy, N is the Riemannian product of a totaZZy geodesic, complex submanifold C Ph and a totaZZy geodesic, totaZZy real submanifold R PP and (c) the immersion in induced from the Segre imbedding.

M+(p) is a totally geodesic submanifold of the symmetric space M= G/H. 2 The normal space Tp M+ (p) of M (p) at p in M is the tangent space of a complete connected totaZZy geodesic submanifold M_(p). It is well-known that every complete totally geodesic submanifold of a symmetric space is a symmetric space. For a symmetric space M the dimension of a maximal flat totally geodesic submanifold of M is called the rank of M, denoted by rk M. From the equation of Gauss, it follows that rk B< rk M if B is totally geodesic in M.

15). 5 (Chen 1979a). 16). 2. Lawson (1970) showed that for any positive integer g, there is a closed minimal surface m in the unit 3-sphere S3 such that the genus of M is g and the area of M is <87r. From this fact, we know that for any closed oriented surface M, there exists an immersion from M into E3 whose total mean curvature is < 87r. 6. Let M be a closed surface which is not homeomorphic to 29 22 S , RP or S1 xS1. 3. The relations between total mean curvature and the theory of variations have been studied in Chen (1972e, 1973a), Willmore and Jhaveri (1972).

Download PDF sample

Geometry of submanifolds and its applications by Bang-yen Chen

by Steven

Rated 4.58 of 5 – based on 17 votes