# The Mixed Scalar Curvature of a Twisted Product Riemannian Manifolds and Projective Submersions

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## Abstract

**:**

## 1. Introduction

## 2. The Mixed Scalar Curvature of Complete Twisted and Warped Products Riemannian Manifolds

**Proposition**

**1.**

**Proof.**

**Proposition**

**2.**

**Proposition**

**3.**

**Proposition**

**4.**

**Theorem**

**1.**

## 3. Projective Submersions

**Theorem**

**2.**

**Proof.**

**Corollary**

**1.**

**Theorem**

**3.**

**Remark**

**1.**

**Corollary**

**2.**

## 4. Appendix

**Lemma**

**1.**

**Proof.**

## 5. Concluding Remarks

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Rovenski, V.; Stepanov, S.; Tsyganok, I.
The Mixed Scalar Curvature of a Twisted Product Riemannian Manifolds and Projective Submersions. *Mathematics* **2019**, *7*, 527.
https://doi.org/10.3390/math7060527

**AMA Style**

Rovenski V, Stepanov S, Tsyganok I.
The Mixed Scalar Curvature of a Twisted Product Riemannian Manifolds and Projective Submersions. *Mathematics*. 2019; 7(6):527.
https://doi.org/10.3390/math7060527

**Chicago/Turabian Style**

Rovenski, Vladimir, Sergey Stepanov, and Irina Tsyganok.
2019. "The Mixed Scalar Curvature of a Twisted Product Riemannian Manifolds and Projective Submersions" *Mathematics* 7, no. 6: 527.
https://doi.org/10.3390/math7060527