• 제목/요약/키워드: curvatures

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LK-BIHARMONIC HYPERSURFACES IN SPACE FORMS WITH THREE DISTINCT PRINCIPAL CURVATURES

  • Aminian, Mehran
    • 대한수학회논문집
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    • 제35권4호
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    • pp.1221-1244
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    • 2020
  • In this paper we consider LK-conjecture introduced in [5, 6] for hypersurface Mn in space form Rn+1(c) with three principal curvatures. When c = 0, -1, we show that every L1-biharmonic hypersurface with three principal curvatures and H1 is constant, has H2 = 0 and at least one of the multiplicities of principal curvatures is one, where H1 and H2 are first and second mean curvature of M and we show that there is not L2-biharmonic hypersurface with three disjoint principal curvatures and, H1 and H2 is constant. For c = 1, by considering having three principal curvatures, we classify L1-biharmonic hypersurfaces with multiplicities greater than one, H1 is constant and H2 = 0, proper L1-biharmonic hypersurfaces which H1 is constant, and L2-biharmonic hypersurfaces which H1 and H2 is constant.

척추의 만곡과 족저부 압력 분포 및 발각도의 상관성 연구 - 족부 진단기의 임상적 활용 가능성 검토를 위한 예비연구 - (A Study of the Correlation between Spinal Curvatures, Plantar Pressure and Foot Angles)

  • 은영준;송윤경;임형호
    • 척추신경추나의학회지
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    • 제2권2호
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    • pp.1-16
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    • 2007
  • Objectives : The purpose of this study was to identify spinal curvatures, plantar pressure and foot angles in a walking. Methods : 19 outpatients under 19 years old were included. Plantar pressure and foot angle in a walking were measured by using Gaitview AFA-50. Spinal curvatures were measured by using radiograph. Results : The cervical lordotic angle is significantly difference with left and right plantar pressure(p=0.027). The thoracic kyphotic angle is significantly difference with left and right plantar pressure(p=0.026). Cobb's angle is significantly difference with left and right plantar pressure(p=0.027). The other plantar pressure were no difference from spinal curvatures and foot angle in a walking. Conclusion : There were no correlation between plantar pressure, spinal curvatures and foot angle. We consider that needed more additional study.

HOMOGENEOUS REAL HYPERSURFACES IN A COMPLEX HYPERBOLIC SPACE WITH FOUR CONSTANT PRINCIPAL CURVATURES

  • Song, Hyunjung
    • 충청수학회지
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    • 제21권1호
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    • pp.29-48
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    • 2008
  • We deal with the classification problem of real hypersurfaces in a complex hyperbolic space. In order to classify real hypersurfaces in a complex hyperbolic space we characterize a real hypersurface M in $H_n(\mathbb{C})$ whose structure vector field is not principal. We also construct extrinsically homogeneous real hypersurfaces with four distinct curvatures and their structure vector fields are not principal.

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LORENTZIAN SURFACES WITH CONSTANT CURVATURES AND TRANSFORMATIONS IN THE 3-DIMENSIONAL LORENTZIAN SPACE

  • Park, Joon-Sang
    • 대한수학회지
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    • 제45권1호
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    • pp.41-61
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    • 2008
  • We study Lorentzian surfaces with the constant Gaussian curvatures or the constant mean curvatures in the 3-dimensional Lorentzian space and their transformations. Such surfaces are associated to the Lorentzian Grassmannian systems and some transformations on such surfaces are given by dressing actions on those systems.

Pseudohermitian Curvatures on Bounded Strictly Pseudoconvex Domains in ℂ2

  • Seo, Aeryeong
    • Kyungpook Mathematical Journal
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    • 제62권2호
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    • pp.323-331
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    • 2022
  • In this paper, we present a formula for pseudohermitian curvatures on bounded strictly pseudoconvex domains in ℂ2 with respect to the coefficients of adapted frames given by Graham and Lee in [3] and their structure equations. As an application, we will show that the pseudohermitian curvatures on strictly plurisubharmonic exhaustions of Thullen domains diverges when the points converge to a weakly pseudoconvex boundary point of the domain.

ON THE SPHERICAL INDICATRIX CURVES OF THE SPACELIKE SALKOWSKI CURVE WITH TIMELIKE PRINCIPAL NORMAL IN LORENTZIAN 3-SPACE

  • Birkan Aksan;Sumeyye Gur Mazlum
    • 호남수학학술지
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    • 제45권3호
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    • pp.513-541
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    • 2023
  • In this paper, we calculate Frenet frames, Frenet derivative formulas, curvatures, arc lengths, geodesic curvatures according to the Lorentzian 3-space ℝ31, Lorentzian sphere 𝕊21 and hyperbolic sphere ℍ20 of the spherical indicatrix curves of the spacelike Salkowski curve with the timelike principal normal in ℝ31 and draw the graphs of these indicatrix curves on the spheres.

SOLITON FUNCTIONS AND RICCI CURVATURES OF D-HOMOTHETICALLY DEFORMED f-KENMOTSU ALMOST RIEMANN SOLITONS

  • Urmila Biswas;Avijit Sarkar
    • 대한수학회논문집
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    • 제38권4호
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    • pp.1215-1231
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    • 2023
  • The present article contains the study of D-homothetically deformed f-Kenmotsu manifolds. Some fundamental results on the deformed spaces have been deduced. Some basic properties of the Riemannian metric as an inner product on both the original and deformed spaces have been established. Finally, applying the obtained results, soliton functions, Ricci curvatures and scalar curvatures of almost Riemann solitons with several kinds of potential vector fields on the deformed spaces have been characterized.

A CHARACTERIZATION OF MAXIMAL SURFACES IN TERMS OF THE GEODESIC CURVATURES

  • Eunjoo Lee
    • 충청수학회지
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    • 제37권2호
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    • pp.67-74
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    • 2024
  • Maximal surfaces have a prominent place in the field of differential geometry, captivating researchers with their intriguing properties. Bearing a direct analogy to the minimal surfaces in Euclidean space, investigating both their similarities and differences has long been an important issue. This paper is aimed to give a local characterization of maximal surfaces in 𝕃3 in terms of their geodesic curvatures, which is analogous to the minimal surface case presented in [8]. We present a classification of the maximal surfaces under some simple condition on the geodesic curvatures of the parameter curves in the line of curvature coordinates.