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Year 2020, Volume: 10 Issue: 2, 494 - 505, 30.12.2020
https://doi.org/10.37094/adyujsci.743557

Abstract

References

  • [1] Chen B.Y., Ogiue K., On totally real submanifolds, Transactions of the American Mathematical Society, 193, 257-266, 1974.
  • [2] Blair D.E., Contact manifolds in Riemannian geometry, Lectures Notes in Mathematics 509, Springer-Verlag, Berlin, 146p, 1976.
  • [3] Yamaguchi S., Kon M., Ikawa T., C-totally real submanifolds, Journal of Differential Geometry, 11, 59-64, 1976.
  • [4] Blair D.E., Ogiue K., Geometry of ıntegral submanifolds of a contact distribution, Illinois Journal of Mathematics, 19, 269-275, 1975.
  • [5] Verheyen P., Verstraelen L., Conformally flat C-totally real submanifolds of Sasakian space forms, Geometriae Dedicata, 12, 163-169, 1982.
  • [6] Tanno S., Ricci Curvatures of Contact Riemannian manifolds, Tôhoku Mathematical Journal, 40, 441-448, 1988.
  • [7] Blair D.E., Ogiue K., Positively curved ıntegral submanifolds of a contact distribution, Illinois Journal of Mathematics, 19, 628-631, 1975.
  • [8] Blair D.E., Koufogiorgos T., Papantoniou, B.J., Contact metric manifolds satisfying a nullity condition, Israel Journal of Mathematics, 91,189-214, 1995.
  • [9] Verstraelen L., Vrancken L., Pinching Theorems for C-Totally Real Submanifolds of Sasakian Space Forms, Journal of Geometry, 33, 172-184, 1988.
  • [10] Koufogiorgos T., Contact Riemannian manifolds with constant 𝜑. -sectional curvature, Geometry and Topology of Submanifolds VIII, World Scientific, 1996, ISBN 981-02-2776-0.
  • [11] Yano K., Kon M., Structures on manifolds, World Scientific, 508p, 1984.
  • [12] Yano K., Kon M., Anti-invariant submanifolds of a Sasakian Space Forms, Tôhoku Mathematical Journal, 29, 9-23, 1976.
  • [13] Yano K., Kon M., Anti-Invariant submanifolds, Marcel Dekker, New York. 185p, 1978.

Conformally Flat Minimal C-Totally Real Submanifolds of (k,μ)-Nullity Space Forms

Year 2020, Volume: 10 Issue: 2, 494 - 505, 30.12.2020
https://doi.org/10.37094/adyujsci.743557

Abstract

Using the expression for the Laplacian of the square of the lenght of the second fundamental form of conformally ‡at minimal C-totally real submanifolds of a(k;)-nullity space form pinchings for scalar curvature and sectional curvature are obtained which imply that the submanifolds must be totally geodesic.

References

  • [1] Chen B.Y., Ogiue K., On totally real submanifolds, Transactions of the American Mathematical Society, 193, 257-266, 1974.
  • [2] Blair D.E., Contact manifolds in Riemannian geometry, Lectures Notes in Mathematics 509, Springer-Verlag, Berlin, 146p, 1976.
  • [3] Yamaguchi S., Kon M., Ikawa T., C-totally real submanifolds, Journal of Differential Geometry, 11, 59-64, 1976.
  • [4] Blair D.E., Ogiue K., Geometry of ıntegral submanifolds of a contact distribution, Illinois Journal of Mathematics, 19, 269-275, 1975.
  • [5] Verheyen P., Verstraelen L., Conformally flat C-totally real submanifolds of Sasakian space forms, Geometriae Dedicata, 12, 163-169, 1982.
  • [6] Tanno S., Ricci Curvatures of Contact Riemannian manifolds, Tôhoku Mathematical Journal, 40, 441-448, 1988.
  • [7] Blair D.E., Ogiue K., Positively curved ıntegral submanifolds of a contact distribution, Illinois Journal of Mathematics, 19, 628-631, 1975.
  • [8] Blair D.E., Koufogiorgos T., Papantoniou, B.J., Contact metric manifolds satisfying a nullity condition, Israel Journal of Mathematics, 91,189-214, 1995.
  • [9] Verstraelen L., Vrancken L., Pinching Theorems for C-Totally Real Submanifolds of Sasakian Space Forms, Journal of Geometry, 33, 172-184, 1988.
  • [10] Koufogiorgos T., Contact Riemannian manifolds with constant 𝜑. -sectional curvature, Geometry and Topology of Submanifolds VIII, World Scientific, 1996, ISBN 981-02-2776-0.
  • [11] Yano K., Kon M., Structures on manifolds, World Scientific, 508p, 1984.
  • [12] Yano K., Kon M., Anti-invariant submanifolds of a Sasakian Space Forms, Tôhoku Mathematical Journal, 29, 9-23, 1976.
  • [13] Yano K., Kon M., Anti-Invariant submanifolds, Marcel Dekker, New York. 185p, 1978.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Physics
Journal Section Mathematics
Authors

Ahmet Yıldız 0000-0002-9799-1781

Publication Date December 30, 2020
Submission Date May 28, 2020
Acceptance Date October 8, 2020
Published in Issue Year 2020 Volume: 10 Issue: 2

Cite

APA Yıldız, A. (2020). Conformally Flat Minimal C-Totally Real Submanifolds of (k,μ)-Nullity Space Forms. Adıyaman University Journal of Science, 10(2), 494-505. https://doi.org/10.37094/adyujsci.743557
AMA Yıldız A. Conformally Flat Minimal C-Totally Real Submanifolds of (k,μ)-Nullity Space Forms. ADYU J SCI. December 2020;10(2):494-505. doi:10.37094/adyujsci.743557
Chicago Yıldız, Ahmet. “Conformally Flat Minimal C-Totally Real Submanifolds of (k,μ)-Nullity Space Forms”. Adıyaman University Journal of Science 10, no. 2 (December 2020): 494-505. https://doi.org/10.37094/adyujsci.743557.
EndNote Yıldız A (December 1, 2020) Conformally Flat Minimal C-Totally Real Submanifolds of (k,μ)-Nullity Space Forms. Adıyaman University Journal of Science 10 2 494–505.
IEEE A. Yıldız, “Conformally Flat Minimal C-Totally Real Submanifolds of (k,μ)-Nullity Space Forms”, ADYU J SCI, vol. 10, no. 2, pp. 494–505, 2020, doi: 10.37094/adyujsci.743557.
ISNAD Yıldız, Ahmet. “Conformally Flat Minimal C-Totally Real Submanifolds of (k,μ)-Nullity Space Forms”. Adıyaman University Journal of Science 10/2 (December 2020), 494-505. https://doi.org/10.37094/adyujsci.743557.
JAMA Yıldız A. Conformally Flat Minimal C-Totally Real Submanifolds of (k,μ)-Nullity Space Forms. ADYU J SCI. 2020;10:494–505.
MLA Yıldız, Ahmet. “Conformally Flat Minimal C-Totally Real Submanifolds of (k,μ)-Nullity Space Forms”. Adıyaman University Journal of Science, vol. 10, no. 2, 2020, pp. 494-05, doi:10.37094/adyujsci.743557.
Vancouver Yıldız A. Conformally Flat Minimal C-Totally Real Submanifolds of (k,μ)-Nullity Space Forms. ADYU J SCI. 2020;10(2):494-505.

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