# Search results for: Y. Nikolayevsky

Mathematische Nachrichten > 293 > 4 > 754 - 760

manuscripta mathematica > 2019 > 158 > 3-4 > 353-370

Linear Algebra and its Applications > 2016 > 504 > C > 574-580

Mathematische Nachrichten > 289 > 2-3 > 321 - 331

Israel Journal of Mathematics > 2015 > 207 > 1 > 361-375

*M*which admits a totally geodesic hypersurface

*F*is isometric to either (a) the Riemannian product of a space of constant curvature and a homogeneous space, or (b) the warped product of the Euclidean space and a homogeneous space, or (c) the twisted product of the line and a homogeneous space (with the warping/twisting function given explicitly)...

Mathematische Zeitschrift > 2015 > 280 > 1-2 > 1-16

Annali di Matematica Pura ed Applicata ( 01923 -) > 2012 > 191 > 4 > 677-709

Differential Geometry and its Applications > 2010 > 28 > 6 > 689-696

Mathematische Annalen > 2005 > 331 > 3 > 505-522

*M*

^{ n }be a Riemannian manifold and

*R*its curvature tensor. For a point

*p*∈

*M*

^{ n }and a unit vector

*X*∈

*T*

_{ p }

*M*

^{ n }, the Jacobi operator is defined by

*R*

_{ X }=

*R*(

*X*,·)

*X*. The manifold

*M*

^{ n }is called

*pointwise Osserman*if, for every

*p*∈

*M*

^{ n }, the spectrum of the Jacobi operator does not depend of the choice of

*X*, and is called

*globally Osserman*if it depends neither of

*X*, nor of

*p*. Osserman conjectured...

manuscripta mathematica > 2004 > 115 > 1 > 31-53

*M*

^{ n }with the curvature tensor

*R*, the Jacobi operator

*R*

_{ X }is defined by

*R*

_{ X }

*Y*=

*R*(

*X*,

*Y*)

*X*. The manifold

*M*

^{ n }is called

*pointwise Osserman*if, for every

*p*∈

*M*

^{ n }, the eigenvalues of the Jacobi operator

*R*

_{ X }do not depend of a unit vector

*X*∈

*T*

_{ p }

*M*

^{ n }, and is called

*globally Osserman*if they do not depend of the point

*p*either. R. Osserman conjectured that globally...

Differential Geometry and its Applications > 2003 > 18 > 3 > 239-253

^{n}be a Riemannian manifold. For a point p M

^{n}and a unit vector X T

_{p}M

^{n}, the Jacobi operator is defined by R

_{X}=R(X,.)X, where R is the curvature tensor. The manifold M

^{n}is called pointwise Osserman if, for every p M

^{n}, the spectrum of the Jacobi operator does not depend of the choice of X, and is called globally Osserman if it...

Discrete & Computational Geometry > 2000 > 23 > 2 > 191-206

*n*vertices and

*m*edges, we show that, for drawings in the plane,

*m≤ (2/3)(n-1)*for thrackles, while

*m≤ 2n-2*for generalized thrackles. This improves theorems of Lovász, Pach, and Szegedy. The paper also examines thrackles in the more...

Discrete & Computational Geometry > 2000 > 23 > 2 > 191-206