Amalgamatic Curvature and Absolutely Umbilical Hypersurfaces
Authors:Charles Conley, Rebecca Etnyre, Brady Gardener, Lucy Odom
Mentor:Bogdan Suceava, Professor of Mathematics, Ph.D., California State University Fullerton
We review the concept of curvature on hypersurfaces and introduce a new curvature invariant called amalgamatic curvature. We explore its geometric interpretation by proving an inequality relating it to the absolute mean curvature of the hypersurface. We obtain a new class of geometric objects: the absolutely umbilical hypersurfaces. We will illustrate this class through examples.