Amalgamatic Curvature and Absolutely Umbilical Hypersurfaces
Authors:
Charles Conley, Rebecca Etnyre, Brady Gardener, Lucy OdomMentor:
Bogdan Suceava, Professor of Mathematics, Ph.D., California State University FullertonWe 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.