We establish several formulas for a 3-dimensional <mml:math alttext="${\mathrm{CR}}$" id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mtext>CR</mml:mtext></mml:math>-submanifold of a six-dimensional
sphere and state some results obtained by making use of them.

Minimal <mml:math alttext="${\mathrm{CR}}$" id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mtext>CR</mml:mtext></mml:math>-submanifolds of a six-dimentional sphere

Minimal <svg style="vertical-align:-0.20473pt" height="11.6875" version="1.1" viewBox="0 0 21.987499 11.6875" width="21.987499" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.363)"><path id="x43" d="M614 175l29 -10q-33 -109 -57 -154q-121 -26 -184 -26q-90 0 -160.5 29t-112.5 77t-63.5 105.5t-21.5 119.5q0 157 108 253t277 96q36 0 71.5 -5t69 -13.5t36.5 -8.5q15 -102 20 -150l-29 -8q-20 79 -66.5 114t-128.5 35q-119 0 -187.5 -86t-68.5 -207&#xA;q0 -140 73.5 -227.5t188.5 -87.5q73 0 119.5 37.5t86.5 116.5z" /></g><g transform="matrix(.017,-0,0,-.017,11.367,11.363)"><path id="x52" d="M631 18l-4 -26q-24 0 -35 1q-57 3 -92.5 23t-69.5 68q-21 30 -101 160q-13 22 -30.5 31t-54.5 9h-32v-159q0 -63 14 -77.5t74 -19.5v-28h-262v28q62 5 76 19.5t14 77.5v402q0 62 -13 76t-73 19v28h248q109 0 159 -34q67 -42 67 -131q0 -115 -127 -172q27 -52 89 -144&#xA;q49 -71 81 -104q31 -36 72 -47zM212 316h48q73 0 108 29q55 42 55 124q0 76 -42 112t-104 36q-41 0 -54 -10q-11 -7 -11 -44v-247z" /></g></svg>-submanifolds of a six-dimentional sphere

International Journal of Mathematics and Mathematical Sciences

Minimal CR-submanifolds of a six-dimentional sphere

Abstract

Copyright