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ON SOME RIEMANNIAN PRODUCT MANIFOLDS
"... Abstract. A fourparametric family of 4dimensional Riemannian product manifolds is constructed on a Lie group. This family is characterized geometrically. The form of the curvature tensor on the manifolds is obtained. ..."
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Abstract. A fourparametric family of 4dimensional Riemannian product manifolds is constructed on a Lie group. This family is characterized geometrically. The form of the curvature tensor on the manifolds is obtained.
Action Classification on Product Manifolds
"... Videos can be naturally represented as multidimensional arrays known as tensors. However, the geometry of the tensor space is often ignored. In this paper, we argue that the underlying geometry of the tensor space is an important property for action classification. We characterize a tensor as a poin ..."
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Cited by 31 (5 self)
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point on a product manifold and perform classification on this space. First, we factorize a tensor relating to each order using a modified High Order Singular Value Decomposition (HOSVD). We recognize each factorized space as a Grassmann manifold. Consequently, a tensor is mapped to a point on a product
Lifts of Structures on Product Manifolds
, 2009
"... This article presents the further steps of the previously done studies taking into consideration the kth order extensions of a complex manifold. In the previous studies higher order vertical and complete lifts of structures on the complex manifold were introduced. Presently, kth extended spaces of ..."
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of a product manifold have been set and the higher order vertical, complete, complete vertical and horizontal lifts of geometric structures on the product manifold have been presented.
Ricci Flow with Surgery on ThreeManifolds
"... This is a technical paper, which is a continuation of [I]. Here we verify most of the assertions, made in [I, §13]; the exceptions are (1) the statement that a 3manifold which collapses with local lower bound for sectional curvature is a graph manifold this is deferred to a separate paper, as the ..."
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Cited by 454 (2 self)
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This is a technical paper, which is a continuation of [I]. Here we verify most of the assertions, made in [I, §13]; the exceptions are (1) the statement that a 3manifold which collapses with local lower bound for sectional curvature is a graph manifold this is deferred to a separate paper
ON STABILITY OF EINSTEIN WARPED PRODUCT MANIFOLDS
"... Abstract. Let (B, ǧ) and (N, ĝ) be Einstein manifolds. Then, we get a complete (necessary and sufficient) condition for the warped product manifold B ×f N: = (B × N, g ̌ + fĝ) to be Einstein, and obtain a complete condition for the Einstein warped product manifold B ×f N to be weakly stable. Mor ..."
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Abstract. Let (B, ǧ) and (N, ĝ) be Einstein manifolds. Then, we get a complete (necessary and sufficient) condition for the warped product manifold B ×f N: = (B × N, g ̌ + fĝ) to be Einstein, and obtain a complete condition for the Einstein warped product manifold B ×f N to be weakly stable
Curvature relations in almost product manifolds
, 1999
"... New relations involving curvature components for the various connections appearing in the theory of almost product manifolds are given and the conformal behaviour of these connections are studied. New identities for the irreducible parts of the deformation tensor are derived. Some direct physical ap ..."
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New relations involving curvature components for the various connections appearing in the theory of almost product manifolds are given and the conformal behaviour of these connections are studied. New identities for the irreducible parts of the deformation tensor are derived. Some direct physical
c © TÜBİTAK Slant submanifolds of Kaehler Product Manifolds
"... In this paper, we study slant submanifolds of a Kaehler product manifold. We show that an Finvariant slant submanifold of Kaehler product manifold is a product manifold. We also obtain some curvature inequalities in terms of scalar curvature and Ricci tensor. ..."
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In this paper, we study slant submanifolds of a Kaehler product manifold. We show that an Finvariant slant submanifold of Kaehler product manifold is a product manifold. We also obtain some curvature inequalities in terms of scalar curvature and Ricci tensor.
Human gesture recognition on product manifolds
 Journal of Machine Learning Research
"... Action videos are multidimensional data and can be naturally represented as data tensors. While tensor computing is widely used in computer vision, the geometry of tensor space is often ignored. The aim of this paper is to demonstrate the importance of the intrinsic geometry of tensor space which yi ..."
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Cited by 8 (0 self)
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yields a very discriminating structure for action recognition. We characterize data tensors as points on a product manifold and model it statistically using least squares regression. To this aim, we factorize a data tensor relating to each order of the tensor using Higher Order Singular Value
Discrete DifferentialGeometry Operators for Triangulated 2Manifolds
, 2002
"... This paper provides a unified and consistent set of flexible tools to approximate important geometric attributes, including normal vectors and curvatures on arbitrary triangle meshes. We present a consistent derivation of these first and second order differential properties using averaging Vorono ..."
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Cited by 453 (17 self)
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This paper provides a unified and consistent set of flexible tools to approximate important geometric attributes, including normal vectors and curvatures on arbitrary triangle meshes. We present a consistent derivation of these first and second order differential properties using averaging Voronoi cells and the mixed FiniteElement/FiniteVolume method, and compare them to existing formulations. Building upon previous work in discrete geometry, these new operators are closely related to the continuous case, guaranteeing an appropriate extension from the continuous to the discrete setting: they respect most intrinsic properties of the continuous differential operators.
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