Communications in Analysis and Geometry

Volume 24 (2016)

Number 4

Austere submanifolds in $\mathbb{C}P^n$

Pages: 821 – 841



Marianty Ionel (Institute of Mathematics, Federal University of Rio de Janeiro, Brazil)

Thomas A. Ivey (Department of Mathematics, College of Charleston, South Carolina, U.S.A.)


For an arbitrary submanifold $M \subset \mathbb{C}P^n$ we determine conditions under which it is austere, i.e., the normal bundle of $M$ is special Lagrangian with respect to Stenzel’s Ricci-flat Kähler metric on $T \, \mathbb{C}P^n$. We also classify austere surfaces in $\mathbb{C}P^n$.

Published 3 November 2016