The Geometry of Submanifolds

By Yu. A. Aminov. 2001

442 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/f61a799474dd1661a5f6773a9598760ca63dc22e

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In Geometry and Topology

Citations in the corpus

Optimal inequalities for the normalized δ-Casorati curvatures of submanifolds in Kenmotsu space forms (2017, background): “Moreover, in computer vision the Casorati curvature occurs as the bending energy; see [16] and also [1; 17; 24; 33; 34] for the geometricalmeaning, importance and various applications of the Casorati curvatures.”
GEOMETRY OF WARPED PRODUCTS AS RIEMANNIAN SUBMANIFOLDS AND RELATED PROBLEMS (2002, unknown): “Then the equation of Gauss is given by (see, for instance, [7]) R(X,Y ;Z,W ) = c{〈X,W 〉〈Y,Z〉 − 〈X,Z〉〈Y,W 〉} + 〈σ(X,W ), σ(Y,Z)〉 − 〈σ(X,Z), σ(Y,W )〉 , (2.”
SUBMANIFOLDS OF GENERALIZED SASAKIAN SPACE FORMS (2009, unknown): “In [10], B.”
SOME RESULTS ON CONCIRCULAR VECTOR FIELDS AND THEIR APPLICATIONS TO RICCI SOLITONS (2015, unknown): “Basic formulas and definitions for submanifolds For general references on Riemannian submanifolds, we refer to [2, 3, 5].”
Classification results for biharmonic submanifolds in spheres (2007, background): “In order to prove that b) implies a), recall that, for m ≥ 4, by a well-known result (see, for example, [4]), any conformally flat hypersurface of a space form is quasi-umbilical and we conclude.”
ON ISOMETRIC MINIMAL IMMERSIONS FROM WARPED PRODUCTS INTO REAL SPACE FORMS (2002, methodology): “Then the equation of Gauss is given by (see, for example, [1])”
Almost Kenmotsu manifolds and local symmetry (2007, background): “Now, each integral manifold M ′ of D is an almost Kähler, totally umbilical submanifold and then it has constant sectional curvature ([7]).”
Defects in conformal field theory (2016, background): “We refer, for instance, to [65] and [66] for more details.”
On the scalar curvature of constant mean curvature hypersurfaces in space forms (2009, background): “m principle is said to hold on an n-dimensional Riemannian manifold Σn if, for any smooth function u∈ C∞(Σ) with u∗ = sup Σ u<+∞ there exists a sequence of points {p k} ∈N in Σ with the properties (5) (i) u(p k) >u∗ − 1 k , (ii) |∇u(p k)| < 1 k , and (iii) ∆u(p k) < 1 k . In this sense, ”