Geodesic
From G\aa rding's cones to $p$-convex hypersurfaces
Contemporary Mathematics. Fundamental Directions, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 1, Tome 45 (2012), pp. 94-104

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We consider cones discovered by Gårding in 1959. They play the fundamental role in the modern theory of fully nonlinear second-order partial differential equations. A new classification of symmetric matrices is presented based on the $m$-positiveness property. Such a classification establishes a new trend in geometry, generating a notion of $m$-convex hypersurfaces. 
@article{CMFD_2012_45_a6,
     author = {N. M. Ivochkina},
     title = {From {G\aa} rding's cones to $p$-convex hypersurfaces},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {94--104},
     publisher = {mathdoc},
     volume = {45},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2012_45_a6/}
}
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N. M. Ivochkina. From G\aa rding's cones to $p$-convex hypersurfaces. Contemporary Mathematics. Fundamental Directions, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 1, Tome 45 (2012), pp. 94-104. http://geodesic.mathdoc.fr/item/CMFD_2012_45_a6/