Geodesic
Extremals of the Dirichlet functional on the manifold of two-dimensional spheroids in SO(3)
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 3, Tome 192 (2021), pp. 94-101

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An approach to the approximate calculation of extremals of the Dirichlet functional on the Banach Lie group of “singular spheroids” defined in an annulus on the coordinate plane centered at the origin is presented. The technique presented is based on the use of a special simplification (functional reduction) of the equation of extremals. It is shown that the functional reduction allows one to obtain a lower estimate for the Morse index of extremals. We use smooth Fredholm functionals with continuous symmetries on smooth Banach manifolds with Riemannian (Hilbert) framings.
Keywords: smooth functional, extremal, continuous symmetry, codifferential, reduction. 
@article{INTO_2021_192_a9,
     author = {T. Yu. Sapronova and S. L. Tsarev},
     title = {Extremals of the {Dirichlet} functional on the manifold of two-dimensional spheroids in {SO(3)}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {94--101},
     publisher = {mathdoc},
     volume = {192},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_192_a9/}
}
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T. Yu. Sapronova; S. L. Tsarev. Extremals of the Dirichlet functional on the manifold of two-dimensional spheroids in SO(3). Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 3, Tome 192 (2021), pp. 94-101. http://geodesic.mathdoc.fr/item/INTO_2021_192_a9/