@article{DESHMUKH_2021, title={ TOTALLY REAL SURFACES IN $S^6$ }, volume={23}, url={https://journals.math.tku.edu.tw/index.php/TKJM/article/view/4522}, DOI={10.5556/j.tkjm.23.1992.4522}, abstractNote={<div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p><span style="font-size: 12.000000pt; font-family: ’TimesNewRomanPSMT’;">The normal bundle</span><span style="font-size: 12.000000pt; font-family: ’DFKaiShu-SB-Estd-BF’;"> $\bar u$ </span><span style="font-size: 12.000000pt; font-family: ’TimesNewRomanPSMT’;">of a totally real surface $</span><span style="font-size: 11.000000pt; font-family: ’TimesNewRomanPSMT’;">M$ </span><span style="font-size: 12.000000pt; font-family: ’TimesNewRomanPSMT’;">in $S^6$ splits as</span><span style="font-size: 12.000000pt; font-family: ’DFKaiShu-SB-Estd-BF’;"> $\bar u</span><span style="font-size: 16.000000pt; font-family: ’TimesNewRomanPSMT’;">= </span><span style="font-size: 12.000000pt; font-family: ’TimesNewRomanPSMT’;">JTM\oplus \bar\mu$</span> <span style="font-size: 12.000000pt; font-family: ’TimesNewRomanPSMT’;">where $TM$ is the tangent bundle of $</span><span style="font-size: 11.000000pt; font-family: ’TimesNewRomanPSMT’;">M$ </span><span style="font-size: 12.000000pt; font-family: ’TimesNewRomanPSMT’;">and  </span><span style="font-size: 11.000000pt; font-family: ’DFKaiShu-SB-Estd-BF’;">$\bar\mu$ </span><span style="font-size: 12.000000pt; font-family: ’TimesNewRomanPSMT’;">is sub­bundle of</span><span style="font-size: 8.000000pt; font-family: ’DFKaiShu-SB-Estd-BF’;"> <span style="font-size: 12.000000pt; font-family: ’DFKaiShu-SB-Estd-BF’;">$\bar u</span>$ </span><span style="font-size: 12.000000pt; font-family: ’TimesNewRomanPSMT’;">which is invariant under the almost complex structure $</span><span style="font-size: 11.000000pt; font-family: ’TimesNewRomanPSMT’;">J$. </span><span style="font-size: 12.000000pt; font-family: ’TimesNewRomanPSMT’;">We study the totally real surfaces </span><span style="font-size: 11.000000pt; font-family: ’TimesNewRomanPSMT’;">M </span><span style="font-size: 12.000000pt; font-family: ’TimesNewRomanPSMT’;">of constant Gaussian curvature </span><span style="font-size: 11.000000pt; font-family: ’TimesNewRomanPSMT’;">K </span><span style="font-size: 12.000000pt; font-family: ’TimesNewRomanPSMT’;">for which the second fundamental form $h(x, y) \in JTM$, and we show that $K </span><span style="font-size: 14.000000pt; font-family: ’TimesNewRomanPSMT’;">= </span><span style="font-size: 12.000000pt; font-family: ’TimesNewRomanPSMT’;">1$ (that is, $M$ is totally geodesic). </span></p> </div> </div> </div>}, number={1}, journal={Tamkang Journal of Mathematics}, author={DESHMUKH, SHARIEF}, year={2021}, month={Jun.}, pages={11–14} }