Characterization of Isoclinic, Transversally Geodesic and Grassmannizable Webs

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this paper, using Nagy’s webs formalism, Frölisher-Nejenhuis theory for derivation associated with vector differential forms, and Grifone’s connection theory for tensorial algebra on the tangent bundle, it is found invariants associated with almost-Grassmann structures and give an interpretation in terms of these invariants, for the isoclinc, transversally geodesic and Grassmanizable webs.

The theme of the paper is actual, and the results seem interesting, mathematically correct, and significant from the point of view of scientific content. I suggest some modifications to correct or to improve the text.

 

Minor Concerns:

1. The paper's abstract should state the paper's importance, gaps, method, and key results. The introduction is too short and raw. It should analyze the recent and related works with their advantages and disadvantages. The gaps should be clear, and the claimed contributions should be well justified.
2. On line 19, please write “…on two facts;” instead of “…on two facts:”,
3. On line 56, please write “…denote them by ${{T}^{h}}$, ${{T}^{\upsilon }}$, and ${{T}^{t}}$.” instead of “…denote them by  ${{T}^{h}}$, ${{T}^{\upsilon }}$ and ${{T}^{t}}$.”,
4. On line 56, please write a period at the end of the sentence given in Definition 2.2, also, check and correct punctuation remarks throughout the article.
5. The numbers (1), (2), (3), and (6) given to the equations in the article are not referenced in the article. Please delete these equation numbers,
6. The Conclusion section is absent. Please add it to the article.
7. Reference number [7] was not cited in the article; uncited references should be deleted or must be cited within the article.
8. There are too many grammatical or vocabulary errors. The language of the paper must be checked in detail. For instance;

In title: Caracterization, geodezic

In the whole paper:   Start with a capital letter for the word grassmann

Line 16,25: caracterization

Line 22: caracterizes

Line 32: Latter

Line 89: we can defined

Line 227: prooves

Line 241: caracterised

Line 268: symmetrical

Line 305: vanises

Line 359: antisymetrization

Line 389: tranversal

Line 391: horizotal

all these words have to be corrected.

 

In conclusion, I recommend acceptance of this article to be published in Axioms after correcting the suggested revisions.

Comments on the Quality of English Language

1. There are too many grammatical or vocabulary errors. The language of the paper must be checked in detail.

Author Response

Report on Suggested Modifications

First, I would like to express my deep gratitude for reading the manuscript, pointing out errors, and suggesting improvements to ensure that this work is published in its best quality. All their remarks have been taken into consideration:

1. The abstract has been revised to support the suggested format and ideas.
2. The introduction has been rearranged to detail the problem more thoroughly and present the results more clearly.
3. A “Conclusion” paragraph has been added, as suggested.
4. The numbering of equations not used later in the text has been removed. In the old version, it’s about equations (1),(2),(3) and (6) and in this version it’s in l 120, l 172, l 176, l 235.
5. A reference that did not add value to the content has been removed. (in the old version its was reference [7]
6. A reference article that was previously missing from the text has been mentioned, and two new references supporting the origin of the theory have been added. It’s mentioned in l 34 and the new references are [16] and [6], l 16 and l 17.
7. All punctuations have been revised as it was asked for example for Definition 2.2, in l 87
8. Typographical errors, spelling mistakes, and some mathematical terminologies and concepts have been corrected, as for example: Characterization, Later, define instead defined in l 110, proves l 242 etc….

 

The authors, J. SAAB and R. ABSI.

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Please see the attached PDF.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

Please see the attached report PDF.

Author Response

Report on Suggested Modifications

First, I would like to express my deep gratitude for reading the manuscript, pointing out errors, and suggesting improvements to ensure that this work is published in its best quality. All their remarks have been taken into consideration:

1. The abstract has been revised to support the suggested format and ideas.
2. The introduction has been rearranged to detail the problem more thoroughly and present the results more clearly.
3. A “Conclusion” paragraph has been added, in order to emphasize the results.
4. All punctuations have been revised as it was asked for example for Definition 2.2, in l 87
5. Typographical errors, spelling mistakes, and some mathematical terminologies and concepts have been corrected, as for example: Characterization, geodesic repeated many times in the manuscript, Later, define instead defined in l 110, proves l 242 etc….

The authors, J. SAAB and R. ABSI.

 

Author Response File: Author Response.docx