Minimal and totally geodesic unit sections of the unit sphere bundles
Abstract
We consider a real vector bundle $\E$ of rank $p$ and a unit sphere bundle $\E_1\subset \E$ over the Riemannian $M^n$ with the Sasaki-type metric. A unit section of $\E_1$ gives rise to a submanifold in $\E_1$. We give some examples of local minimal unit sections and present a complete description of local totally geodesic unit sections of $\E_1$ in the simplest non-trivial case $p=2$ and $n=2$.
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References
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