162 research outputs found
Bi-Legendrian manifolds and paracontact geometry
We study the interplays between paracontact geometry and the theory of
bi-Legendrian manifolds. We interpret the bi-Legendrian connection of a
bi-Legendrian manifold M as the paracontact connection of a canonical
paracontact structure induced on M and then we discuss many consequences of
this result both for bi-Legendrian and for paracontact manifolds. Finally new
classes of examples of paracontact manifolds are presented.Comment: to appear in Int. J. Geom. Meth. Mod. Phy
On compact holomorphically pseudosymmetric K\"ahlerian manifolds
For compact K\"ahlerian manifolds, the holomorphic pseudosymmetry reduces to
the local symmetry if additionally the scalar curvature is constant and the
structure function is non-negative. Similarly, the holomorphic
Ricci-pseudosymmetry reduces to the Ricci-symmetry under these additional
assumptions. We construct examples of non-compact essentially holomorphically
pseudosymmetric K\"ahlerian manifolds. These examples show that the compactness
assumption cannot be omitted in the above stated theorem.
Recently, the first examples of compact, simply connected essentially
holomorphically pseudosymmetric K\"ahlerian manifolds are discovered by W.
Jelonek. In his examples, the structure functions change their signs on the
manifold
A splitting theorem for Kahler manifolds whose Ricci tensors have constant eigenvalues
It is proved that a compact Kahler manifold whose Ricci tensor has two
distinct, constant, non-negative eigenvalues is locally the product of two
Kahler-Einstein manifolds. A stronger result is established for the case of
Kahler surfaces. Irreducible Kahler manifolds with two distinct, constant
eigenvalues of the Ricci tensor are shown to exist in various situations: there
are homogeneous examples of any complex dimension n > 1, if one eigenvalue is
negative and the other positive or zero, and of any complex dimension n > 2, if
the both eigenvalues are negative; there are non-homogeneous examples of
complex dimension 2, if one of the eigenvalues is zero. The problem of
existence of Kahler metrics whose Ricci tensor has two distinct, constant
eigenvalues is related to the celebrated (still open) Goldberg conjecture.
Consequently, the irreducible homogeneous examples with negative eigenvalues
give rise to complete, Einstein, strictly almost Kahler metrics of any even
real dimension greater than 4.Comment: 18 pages; final version; accepted for publication in International
Journal of Mathematic
Natural Diagonal Riemannian Almost Product and Para-Hermitian Cotangent Bundles
We obtain the natural diagonal almost product and locally product structures
on the total space of the cotangent bundle of a Riemannian manifold. We find
the Riemannian almost product (locally product) and the (almost) para-Hermitian
cotangent bundles of natural diagonal lift type. We prove the characterization
theorem for the natural diagonal (almost) para-K\"ahlerian structures on the
total spaces of the cotangent bundle.Comment: 10 pages, will appear in Czechoslovak Mathematical Journa
Almost Contact Lagrangian Submanifolds of Nearly Kaehler 6-Sphere
For a Lagrangian submanifold M of S 6 with nearly Kaehler structure, we provide conditions for a canonically induced almost contact metric structure on M by a unit vector field, to be Sasakian. Assuming M contact metric, we show that it is Sasakian if and only if the second fundamental form annihilates the Reeb vector field ξ, furthermore, if the Sasakian submanifold M is parallel along ξ, then it is the totally geodesic 3-sphere. We conclude with a condition that reduces the normal canonical almost contact metric structure on M to Sasakian or cosymplectic structure
The curvature tensor of almost cosymplectic and almost Kenmotsu (\kappa,\mu,\nu)-spaces
We study the Riemann curvature tensor of (\kappa,\mu,\nu)-spaces when they
have almost cosymplectic and almost Kenmotsu structures, giving its writing
explicitly. This leads to the definition and study of a natural generalisation
of the contact metric (\kappa,\mu,\nu)-spaces. We present examples or
obstruction results of these spaces in all possible cases
3-quasi-Sasakian manifolds
In the present paper we carry on a systematic study of 3-quasi-Sasakian
manifolds. In particular we prove that the three Reeb vector fields generate an
involutive distribution determining a canonical totally geodesic and Riemannian
foliation. Locally, the leaves of this foliation turn out to be Lie groups:
either the orthogonal group or an abelian one. We show that 3-quasi-Sasakian
manifolds have a well-defined rank, obtaining a rank-based classification.
Furthermore, we prove a splitting theorem for these manifolds assuming the
integrability of one of the almost product structures. Finally, we show that
the vertical distribution is a minimum of the corrected energy.Comment: 17 pages, minor modifications, references update
Riemannian submersions from almost contact metric manifolds
In this paper we obtain the structure equation of a contact-complex
Riemannian submersion and give some applications of this equation in the study
of almost cosymplectic manifolds with Kaehler fibres.Comment: Abh. Math. Semin. Univ. Hamb., to appea
Killing-Yano tensors and some applications
The role of Killing and Killing-Yano tensors for studying the geodesic motion
of the particle and the superparticle in a curved background is reviewed.
Additionally the Papadopoulos list [74] for Killing-Yano tensors in G
structures is reproduced by studying the torsion types these structures admit.
The Papadopoulos list deals with groups G appearing in the Berger
classification, and we enlarge the list by considering additional G structures
which are not of the Berger type. Possible applications of these results in the
study of supersymmetric particle actions and in the AdS/CFT correspondence are
outlined.Comment: 36 pages, no figure
A conceptual framework for the adoption of big data analytics by e-commerce startups: a case-based approach
E-commerce start-ups have ventured into emerging economies and are growing at a significantly faster pace. Big data has acted like a catalyst in their growth story. Big data analytics (BDA) has attracted e-commerce firms to invest in the tools and gain cutting edge over their competitors. The process of adoption of these BDA tools by e-commerce start-ups has been an area of interest as successful adoption would lead to better results. The present study aims to develop an interpretive structural model (ISM) which would act as a framework for efficient implementation of BDA. The study uses hybrid multi criteria decision making processes to develop the framework and test the same using a real-life case study. Systematic review of literature and discussion with experts resulted in exploring 11 enablers of adoption of BDA tools. Primary data collection was done from industry experts to develop an ISM framework and fuzzy MICMAC analysis is used to categorize the enablers of the adoption process. The framework is then tested by using a case study. Thematic clustering is performed to develop a simple ISM framework followed by fuzzy analytical network process (ANP) to discuss the association and ranking of enablers. The results indicate that access to relevant data forms the base of the framework and would act as the strongest enabler in the adoption process while the company rates technical skillset of employees as the most important enabler. It was also found that there is a positive correlation between the ranking of enablers emerging out of ISM and ANP. The framework helps in simplifying the strategies any e-commerce company would follow to adopt BDA in future. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature
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