Author
George Kaimakamis
Other affiliations: Hellenic Military Academy, University of Patras
Bio: George Kaimakamis is an academic researcher from Army and Navy Academy. The author has contributed to research in topic(s): Complex space & Hypersurface. The author has an hindex of 8, co-authored 35 publication(s) receiving 255 citation(s). Previous affiliations of George Kaimakamis include Hellenic Military Academy & University of Patras.
Papers
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TL;DR: In this article, it was shown that every nonsmooth hypersurface M13 of E14 with harmonic mean curvature vector is minimal, where H denotes the mean curvatures vector field and L is the Laplacian of induced pseudo-Riemannian metric.
Abstract: A submanifold Mrn of pseudo-Euclidean space Es4 is said to have harmonic mean curvature vector if ?H = 0, where H denotes the mean curvature vector field and ? the Laplacian of the induced pseudo-Riemannian metric. We prove that every nondegenerate Lorentz hypersurface M13 of E14 with harmonic mean curvature vector is minimal.
43 citations
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TL;DR: In this paper, the problem of finding explicitly the helicoidal surfaces of the Minkowski space R 1 3 with prescribed Gaussian or mean curvature given by smooth functions is solved.
Abstract: In this paper we solve the problem of finding explicitly the helicoidal surfaces of the Minkowski space R 1 3 with prescribed Gaussian or mean curvature given by smooth functions. We distinguish three kinds of helicoidal surfaces corresponding to the space-like, time-like or light-like axes of revolution and give some geometric meanings of the helicoidal surfaces of the space-like type. We also define certain solinoid (tubular) surfaces of type I− around a hyperbolic helix in R 1 3 and study some of their geometric properties.
42 citations
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TL;DR: In this paper, the notion of *-Ricci soliton is introduced and real hypersurfaces in non-flat complex space forms admitting a *-ricci s soliton with potential vector field being the structure vector field.
Abstract: In this paper the notion of *-Ricci soliton is introduced and real hypersurfaces in non-flat complex space forms admitting a *-Ricci soliton with potential vector field being the structure vector field ξ are studied. At the end of the paper discussion on this new notion and ideas for further work are presented.
31 citations
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TL;DR: In this paper, it was shown that for every non-degenerate hypersurface of E s 4 the shape operator of which is diagonalizable, with harmonic mean curvature vector field, is minimal.
Abstract: A submanifold M r n of a semi-Euclidean space E s m is said to have harmonic mean curvature vector field if Δ H → = 0 → , where H → denotes the mean curvature vector; submanifolds with harmonic mean curvature vector are also known as biharmonic submanifolds. In this paper, we prove that every nondegenerate hypersurface of E s 4 the shape operator of which is diagonalizable, with harmonic mean curvature vector field, is minimal.
30 citations
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TL;DR: In this article, it was shown that a hypersurface of the pseudo-Euclidean space E s 4 with Δ H → = λ H → and diagonalizable shape operator has constant mean curvature.
Abstract: Submanifolds satisfying Δ H → = λ H → are named by B. Y. Chen submanifolds with proper mean curvature vector. We prove that a hypersurface of the pseudo-Euclidean space E s 4 with Δ H → = λ H → and diagonalizable shape operator, has constant mean curvature.
24 citations
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TL;DR: In this paper, the authors focus their attention on bi-harmonic submanifolds such that the inclusion map is a biharmonic map, i.e. a non-minimal bi-harmonic map with constant sectional curvature.
Abstract: is linear, thusany harmonic map is biharmonic. We call proper biharmonic the non-harmonicbiharmonic maps.In this paper we shall focus our attention on biharmonic submanifolds, i.e. onsubmanifolds such that the inclusion map is a biharmonic map. In this context, aproper biharmonic submanifold is a non-minimal biharmonic submanifold.The first ambient spaces to look for proper biharmonic submanifolds are the spacesof constant sectional curvature c, which we shall denote by E
84 citations
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TL;DR: In this paper, it was shown that the bi-harmonic conjecture is true for δ ( 2 ) -ideal and δ( 3 )-ideal hypersurfaces of a Euclidean space of arbitrary dimension.
Abstract: Let x : M → E m be an isometric immersion from a Riemannian n-manifold into a Euclidean m-space. Denote by Δ and x → the Laplace operator and the position vector of M, respectively. Then M is called biharmonic if Δ 2 x → = 0 . The following Chenʼs Biharmonic Conjecture made in 1991 is well-known and stays open: The only biharmonic submanifolds of Euclidean spaces are the minimal ones. In this paper we prove that the biharmonic conjecture is true for δ ( 2 ) -ideal and δ ( 3 ) -ideal hypersurfaces of a Euclidean space of arbitrary dimension.
67 citations
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TL;DR: In this article, an additional family of marginally trapped Lorentzian flat surfaces in E 2 4 given in Theorem 4.1 of Chen et al. was added to the list.
Abstract: Due to omission, an additional family shall be added to the list of marginally trapped Lorentzian flat surfaces in E 2 4 given in Theorem 4.1 of [B.-Y. Chen, Classification of marginally trapped Lorentzian flat surfaces in E 2 4 and its application to biharmonic surfaces, J. Math. Anal. Appl. 340 (2008) 861–875].
47 citations