论文标题
标态曲率，注射率半径和浸入少量基本形式的浸入
Scalar Curvature, Injectivity Radius and Immersions with Small Second Fundamental Forms
论文作者
论文摘要
在特殊情况下，我们证明了以下内容。 $ \ bullet_ {sc} $在{\ it Injectitivity radii}的“拓扑上复杂”的riemannian $ n $ n $ -manifolds $ x $上，其中$ x $的标态曲率从下面界限为 $ sc（x）\geqσ> 0 $。 $ \ bullet_ {curv} $在{\ it焦点radii}上的下限，从$ k $ -manifolds，例如， $ k $ -torus的同构，与尺寸的某些riemannian歧管$ n = k+m $，例如到圆柱体$ s^{n-1} \ times \ mathbb r^1 $。 $ \ bullet_ {mean} $在Riemannian歧管中域的平均曲率上的拓扑下限。例如在Euclidean $ n $ -space $ \ Mathbb r^n $中。 目前，我们的结果受{\ it旋转条件}和{\ it $ n \ leq 8 $限制的限制。}
We prove in special cases the following. $\bullet_{Sc}$ Bounds on the {\it injectivity radii} of "topologically complicated" Riemannian $n$-manifolds $X$, where the scalar curvatures of $X$ are bounded from below, $Sc(X)\geq σ>0$. $\bullet_{curv}$ Lower bounds on {\it focal radii} of smooth immersions from $k$-manifolds, e.g. homeomorphic to the $k$-torus, to certain Riemannian manifolds of dimensions $n=k+m$, e.g. to the cylinders $S^{n-1} \times \mathbb R^1$. $\bullet_{mean}$ Topological lower bounds on the mean curvatures of domains in Riemannian manifolds. e.g. in the Euclidean $n$-space $\mathbb R^n$. At the present moment, our results are limited by the {\it spin condition} and the {\it $n\leq 8$ restriction.}
