The first and second variation of arc length, Jacobi fields conjugate points, comparison theorems of Morse and Rauch, Myer's theorem on compactness of Riemannian Manifolds. Variation of immersion, Normal variation, first and second variation of the area function, Minimal submanifolds, stability of minimal submanifolds, Index of minimal submanifolds, minimal submanifolds in spheres, complex submanifolds of a complex projective space.
Recommended Books & Papers:
1) Riemannian Geometry, By M. P. DoCarmo, Birkhauser (1992)
2) Minimal Submanifolds and Related Topics, By Y. L. Xin, World Scientific (2003)
3) J. Simon, Minimal verieties in Riemannian manifolds, Ann. Mth. 88(1968), 62-105.
4) S.S Chern, M.P.DoCarmo and S. Kobayashi, Minimal submanifolds of a sphere with second fundamental form of constant length, Functional Analysis and Related topics, Springer Verlag (1970),59-75.