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Submanifolds in Metric Manifolds, 2nd Edition
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Submanifolds in Metric Manifolds, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "B: Geometry and Topology".

Deadline for manuscript submissions: 31 March 2026 | Viewed by 2576

Special Issue Editor

Dr. Cristina-Elena Hretcanu

E-Mail Website
Guest Editor
Faculty of Food Engineering, Stefan cel Mare University of Suceava, 720229 Suceava, Romania
Interests: mathematics; statistics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue, “Submanifolds in Metric Manifolds, 2nd Edition”, will be devoted to the study of an important topic of research in differential geometry, regarding the structure induced on submanifolds by the structure defined on various ambient manifolds.

We call for research articles and review articles focused on issues such as: submanifolds of Riemannian manifolds, submanifolds of Kaehlerian manifolds, submanifolds of Sasakian manifolds, or submanifolds in any types of metric manifolds.

The geometry of any particular submanifolds, such as invariant (or holomorphic) submanifolds; anti-invariant (totally real) submanifolds; semi-invariant submanifolds; slant, semi (or hemi)-slant submanifolds; and warped product (bi-warped, semi-slant, or hemi-slant warped product) submanifolds of metric manifolds endowed by structures can be covered in this Special Issue, with examples and applications (characterization properties and inequalities or equalities cases).

Dr. Cristina-Elena Hretcanu
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • differentiable manifolds
  • Riemannian manifolds
  • Kaehlerian manifolds
  • Sasakian manifolds
  • metric spaces with differentiable structure
  • invariant (or holomorphic) submanifolds
  • anti-invariant (totally real) submanifolds
  • semi-invariant submanifolds
  • slant, semi (or hemi)-slant submanifolds
  • warped product (bi-warped, semi-slant, or hemi- slant warped product) submanifolds
  • totally geodesic, totally umbilical or minimal submanifolds

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Related Special Issue

Published Papers (3 papers)

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Research

30 pages, 435 KB  
Article
Classification of Four-Dimensional CR Submanifolds of the Homogenous Nearly Kähler S3×S3 Which Almost Complex Distribution Is Almost Product Orthogonal on Itself
by Nataša Djurdjević
Mathematics 2025, 13(16), 2638; https://doi.org/10.3390/math13162638 - 17 Aug 2025
Viewed by 429
Abstract
The product manifold S3×S3, which belongs to the homogenous six-dimensional nearly Kähler manifolds, admits two structures, the almost complex structure J and the almost product structure P. The investigation of embeddings of different classes of CR submanifolds [...] Read more.
The product manifold S3×S3, which belongs to the homogenous six-dimensional nearly Kähler manifolds, admits two structures, the almost complex structure J and the almost product structure P. The investigation of embeddings of different classes of CR submanifolds of S3×S3 was started some time ago by investigating three-dimensional CR submanifolds. It resulted that the almost product structure P is very important for the study of CR submanifolds of S3×S3, since submanifolds characterized by different actions of the almost product structure on base vector fields often appear as a result of the study of some specific types of CR submanifolds. Therefore, the investigation of four-dimensional CR submanifolds of S3×S3 is initiated in this article. The main result is the classification of four-dimensional CR submanifolds of S3×S3, whose almost complex distribution D1 is almost product orthogonal on itself. First, it was proved that such submanifolds have a non-integrable almost complex distribution, and then it was proved that these submanifolds are locally product manifolds of curves and three-dimensional CR submanifolds of S3×S3 of the same type, and they were therefore constructed in this way. Full article
(This article belongs to the Special Issue Submanifolds in Metric Manifolds, 2nd Edition)
22 pages, 887 KB  
Article
On the Special Viviani’s Curve and Its Corresponding Smarandache Curves
by Yangke Deng, Yanlin Li, Süleyman Şenyurt, Davut Canlı and İremnur Gürler
Mathematics 2025, 13(9), 1526; https://doi.org/10.3390/math13091526 - 6 May 2025
Cited by 2 | Viewed by 933
Abstract
In the present paper, the special Viviani’s curve is revisited in the context of Smarandache geometry. Accordingly, the paper first defines the special Smarandache curves of Viviani’s curve, including the Darboux vector. Then, it expresses the resulting Frenet apparatus for each Smarandache curve [...] Read more.
In the present paper, the special Viviani’s curve is revisited in the context of Smarandache geometry. Accordingly, the paper first defines the special Smarandache curves of Viviani’s curve, including the Darboux vector. Then, it expresses the resulting Frenet apparatus for each Smarandache curve in terms of the Viviani’s curve. The paper is also supported by extensive graphical representations of Viviani’s curve and its Smarandache curves, as well as their respective curvatures. Full article
(This article belongs to the Special Issue Submanifolds in Metric Manifolds, 2nd Edition)
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18 pages, 324 KB  
Article
On the Geometry of Semi-Invariant Submanifolds in (α, p)-Golden Riemannian Manifolds
by Cristina Elena Hreţcanu and Simona-Luiza Druţă-Romaniuc
Mathematics 2024, 12(23), 3735; https://doi.org/10.3390/math12233735 - 27 Nov 2024
Cited by 1 | Viewed by 790
Abstract
The main aim of this paper is to study some properties of submanifolds in a Riemannian manifold equipped with a new structure of golden type, called the (α, p)-golden structure, which generalizes the almost golden structure (for [...] Read more.
The main aim of this paper is to study some properties of submanifolds in a Riemannian manifold equipped with a new structure of golden type, called the (α, p)-golden structure, which generalizes the almost golden structure (for α=1) and the almost complex golden structure (for α=−1). We present some characterizations of isometrically immersed submanifolds in an (α, p)-golden Riemannian manifold, especially in the case of the semi-invariant submanifolds, and we find some conditions for the integrability of the distributions. Full article
(This article belongs to the Special Issue Submanifolds in Metric Manifolds, 2nd Edition)
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