The stability and the index of compact minimal submanifolds Berger spheres \({\mathbb {S}}^{2n+1}_{\tau },\, 0<\tau \le 1\), are studied. Unlike case standard sphere (\(\tau =1\)), where there no stable submanifolds, have ones if only \(\tau ^2\le 1/2\). Moreover, d-dimensional {S}}^{2n+1}_\tau \) when \(1 / (d+1) < \tau ^2 1\) classified for ^2=1 (d+1)\) submanifold is embedded. Finally, orien...

Abstract Consider a proper, isometric action by unimodular locally compact group G on Riemannian manifold M with boundary, such that / is compact. Then an equivariant Dirac-type operator D under suitable boundary condition has index $${{\,\mathrm{index}\,}}_G(D)$$ index <m...

In [EE1] and [EE2] we presented the solution to the index problem for a natural class of hypoelliptic differential operators on compact contact manifolds. The methods developed to deal with that problem have wider applicability to the index theory of hypoelliptic Fredholm operators. As an example of the power of the proof techniques we present here a new proof of a little known index theorem of...

A high-data-rate $D$ -band transmitter (TX) module cointegrating a dual-channel TX integrated circuit (IC) in 45-nm CMOS partially deplated silicon-on-insulator (PDSOI) technology and an antenna is presented. The proposed system-in-pa...