The golden mean in the topology of four-manifolds, in conformal field theory, in the mathematical probability theory and in Cantorian space-time

Marek-Crnjac, L.

doi:10.1016/j.chaos.2005.08.160

Cited by 18 publications

(5 citation statements)

References 8 publications

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“…In the last few years, the Golden proportion has played an increasing role in modern physical research and it has a unique significant role in atomic physics [20]. The Golden proportion has also interesting properties in topology of four-manifolds, in conformal field theory, in mathematical probability theory and in Cantorian spacetime [23,24]. Inspired by Golden Ratio, a new structure on a Riemannian manifold which named the golden structure was constructed by M. Crasmareanu and C. Hretcanu [4,18,19].…”

Section: The Famous Golden Sectionmentioning

confidence: 99%

On the geometry of the rescaled Riemannian metric on tensor bundles of arbitrary type

Gezer¹,

Altunbaş²

2015

Kodai Math. J.

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Abstract. Let (M, g) be an n−dimensional Riemannian manifold and T 1 1 (M ) be its (1, 1)−tensor bundle equipped with the rescaled Sasaki type metric S g f which rescale the horizontal part by a nonzero differentiable function f . In the present paper, we discuss curvature properties of the Levi-Civita connection and another metric connection of T 1 1 (M ). We construct almost paracomplex Norden structures on T 1 1 (M ) and investigate conditions for these structures to be para-Kähler (paraholomorphic) and quasi-Kähler. Also, some properties of almost paracomplex Norden structures in context of almost product Riemannian manifolds are presented. Finally we introduce the rescaled Sasaki type metric S g f on the (p, q)− tensor bundle and characterize the geodesics on the (p, q)-tensor bundle with respect to the Levi-Civita connection of S g f and another metric connection of S g f .

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Section: The Famous Golden Sectionmentioning

confidence: 99%

On the geometry of the rescaled Riemannian metric on tensor bundles of arbitrary type

Gezer¹,

Altunbaş²

2015

Kodai Math. J.

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“…In the past few years, the golden ratio has played a more and more significant role in modern physical research and atomic physics [2]. The golden ratio also has interesting properties in topology of four-manifolds, in conformal field theory, in mathematical probability theory, in Cantorian spacetime [3], and in differential geometry.…”

Section: Introductionmentioning

confidence: 99%

A Class of Special Hypersurfaces in Real Space Forms

Liu¹

2016

Journal of Function Spaces

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“…In the past few years, the Golden ratio has played a more and more significant role in modern physical research and atomic physics [4]. The Golden ratio also has interesting properties in topology of four-manifolds, in conformal field theory, in mathematical probability theory, in Cantorian spacetime [7] and in differential geometry.…”

Section: Introductionmentioning

confidence: 99%