Normal
0
false
false
false
EN-US
X-NONE
X-NONE
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Table Normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-parent:"";
mso-padding-alt:0in 5.4pt 0in 5.4pt;
mso-para-margin:0in;
mso-para-margin-bottom:.0001pt;
mso-pagination:widow-orphan;
font-size:10.0pt;
font-family:"Times New Roman",serif;}
Absolute total curvature is an invariant of an immersed submanifold of Euclidean space, first studied by Chern and Lashof. Although it has a simple definition in terms of the second fundamental form, bounds on the absolute total curvature imply strong bounds on the complexity of the topology of the manifold, and the equality case has a simple characterization. We will discuss the definition of the absolute total curvature, some related background on isometric immersions, and the proofs of the original theorems by Chern and Lashof relating absolute total curvature bounds to the topology of the submanifold.